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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 72d218235f
commit f23f22d71c
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3
Task/Almost-prime/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Almost_prime
note: Prime Numbers

17
Task/Almost-prime/00-TASK.txt Normal file
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A &nbsp; [[wp:Almost prime|k-Almost-prime]] &nbsp; is a natural number &nbsp; <math>n</math> &nbsp; that is the product of &nbsp; <math>k</math> &nbsp; (possibly identical) primes.
;Example:
1-almost-primes, &nbsp; where &nbsp; <math>k=1</math>, &nbsp; are the prime numbers themselves.
<br>2-almost-primes, &nbsp; where &nbsp; <math>k=2</math>, &nbsp; are the &nbsp; [[Semiprime|semiprimes]].
;Task:
Write a function/method/subroutine/... that generates k-almost primes and use it to create a table here of the first ten members of k-Almost primes for &nbsp; <math>1 <= K <= 5</math>.
;Related tasks:
* &nbsp; [[Semiprime]]
* &nbsp; [[:Category:Prime Numbers]]
<br><br>

21
Task/Almost-prime/11l/almost-prime.11l Normal file
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F k_prime(k, =n)
V f = 0
V p = 2
L f < k & p * p <= n
L n % p == 0
n /= p
f++
p++
R f + (I n > 1 {1} E 0) == k
F primes(k, n)
V i = 2
[Int] list
L list.len < n
I k_prime(k, i)
list [+]= i
i++
R list
L(k) 1..5
print(‘k = ’k‘: ’primes(k, 10))

41
Task/Almost-prime/ALGOL-68/almost-prime.alg Normal file
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BEGIN
INT examples=10, classes=5;
MODE SEMIPRIME = STRUCT ([examples]INT data, INT count);
[classes]SEMIPRIME semi primes;
PROC num facs = (INT n) INT :
COMMENT
Return number of not necessarily distinct prime factors of n.
Not very efficient for large n ...
COMMENT
BEGIN
INT tf := 2, residue := n, count := 1;
WHILE tf < residue DO
INT remainder = residue MOD tf;
( remainder = 0 | count +:= 1; residue %:= tf | tf +:= 1 )
OD;
count
END;
PROC update table = (REF []SEMIPRIME table, INT i) BOOL :
COMMENT
Add i to the appropriate row of the table, if any, unless that row
is already full. Return a BOOL which is TRUE when all of the table
is full.
COMMENT
BEGIN
INT k := num facs(i);
IF k <= classes
THEN
INT c = 1 + count OF table[k];
( c <= examples | (data OF table[k])[c] := i; count OF table[k] := c )
FI;
INT sum := 0;
FOR i TO classes DO sum +:= count OF table[i] OD;
sum < classes * examples
END;
FOR i TO classes DO count OF semi primes[i] := 0 OD;
FOR i FROM 2 WHILE update table (semi primes, i) DO SKIP OD;
FOR i TO classes
DO
printf (($"k = ", d, ":", n(examples)(xg(0))l$, i, data OF semi primes[i]))
OD
END

44
Task/Almost-prime/ALGOL-M/almost-prime.alg Normal file
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begin
integer function mod(a, b);
integer a, b;
mod := a-(a/b)*b;
integer function kprime(n, k);
integer n, k;
begin
integer p, f;
f := 0;
p := 2;
while f < k and p*p <= n do
begin
while mod(n,p) = 0 do
begin
n := n / p;
f := f + 1;
end;
p := p + 1;
end;
if n > 1 then f := f + 1;
if f = k then kprime := 1 else kprime := 0;
end;
integer i, c, k;
for k := 1 step 1 until 5 do
begin
write("k =");
writeon(k);
writeon(": ");
c := 0;
i := 2;
while c < 10 do
begin
if kprime(i, k) <> 0 then
begin
writeon(i);
c := c + 1;
end;
i := i + 1;
end;
end;
end

37
Task/Almost-prime/ALGOL-W/almost-prime.alg Normal file
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begin
logical procedure kPrime( integer value nv, k ) ;
begin
integer p, f, n;
n := nv;
f := 0;
while f <= k and not odd( n ) do begin
n := n div 2;
f := f + 1
end while_not_odd_n ;
p := 3;
while f <= k and p * p <= n do begin
while n rem p = 0 do begin
n := n div p;
f := f + 1
end while_n_rem_p_eq_0 ;
p := p + 2
end while_f_le_k_and_p_is_a_factor ;
if n > 1 then f := f + 1;
f = k
end kPrime ;
begin
for k := 1 until 5 do begin
integer c, i;
write( i_w := 1, s_w := 0, "k = ", k , ": " );
c := 0;
i := 2;
while c < 10 do begin
if kPrime( i, k ) then begin
writeon( i_w := 3, s_w := 0, " ", i );
c := c + 1
end if_kPrime_i_k ;
i := i + 1
end while_c_lt_10
end for_k
end
end.

1
Task/Almost-prime/APL/almost-prime.apl Normal file
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f←{↑r⊣⍵∘{r,∘⊂←⍺↑∪{⍵[⍋⍵]},f∘.×⍵}⍣(⍺-1)⊃r←⊂f←pco¨⍳⍵}

221
Task/Almost-prime/ARM-Assembly/almost-prime.arm Normal file
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/* ARM assembly Raspberry PI */
/* program kprime.s */
/************************************/
/* Constantes */
/************************************/
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
.equ MAXI, 10
.equ MAXIK, 5
/*********************************/
/* Initialized data */
/*********************************/
.data
sMessDeb: .ascii "k="
sMessValeurDeb: .fill 11, 1, ' ' @ size => 11
sMessResult: .ascii " "
sMessValeur: .fill 11, 1, ' ' @ size => 11
szCarriageReturn: .asciz "\n"
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
mov r3,#1 @ k
1: @ start loop k
mov r0,r3
ldr r1,iAdrsMessValeurDeb
bl conversion10 @ call conversion decimal
ldr r0,iAdrsMessValeurDeb
mov r1,#':'
strb r1,[r0,#2] @ write : after k value
mov r1,#0
strb r1,[r0,#3] @ final zéro
ldr r0,iAdrsMessDeb
bl affichageMess @ display message
mov r4,#2 @ n
mov r5,#0 @ result counter
2: @ start loop n
mov r0,r4
mov r1,r3
bl kprime @ is kprine ?
cmp r0,#0
beq 3f @ no
mov r0,r4
ldr r1,iAdrsMessValeur
bl conversion10 @ call conversion decimal
ldr r0,iAdrsMessValeur
mov r1,#0
strb r1,[r0,#4] @ final zéro
ldr r0,iAdrsMessResult
bl affichageMess @ display message
add r5,#1 @ increment counter
3:
add r4,#1 @ increment n
cmp r5,#MAXI @ maxi ?
blt 2b @ no -> loop
ldr r0,iAdrszCarriageReturn
bl affichageMess @ display carriage return
add r3,#1 @ increment k
cmp r3,#MAXIK @ maxi ?
ble 1b @ no -> loop
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrsMessValeur: .int sMessValeur
iAdrszCarriageReturn: .int szCarriageReturn
iAdrsMessResult: .int sMessResult
iAdrsMessValeurDeb: .int sMessValeurDeb
iAdrsMessDeb: .int sMessDeb
/******************************************************************/
/* compute kprime (n,k) */
/******************************************************************/
/* r0 contains n */
/* r1 contains k */
kprime:
push {r1-r7,lr} @ save registers
mov r5,r0 @ save n
mov r7,r1 @ save k
mov r4,#0 @ counter product
mov r1,#2 @ divisor
1: @ start loop
cmp r4,r7 @ counter >= k
bge 4f @ yes -> end
mul r6,r1,r1 @ compute product
cmp r6,r5 @ > n
bgt 4f @ yes -> end
2: @ start loop division
mov r0,r5 @ dividende
bl division @ by r1
cmp r3,#0 @ remainder = 0 ?
bne 3f @ no
mov r5,r2 @ yes -> n = n / r1
add r4,#1 @ increment counter
b 2b @ and loop
3:
add r1,#1 @ increment divisor
b 1b @ and loop
4: @ end compute
cmp r5,#1 @ n > 1
addgt r4,#1 @ yes increment counter
cmp r4,r7 @ counter = k ?
movne r0,#0 @ no -> no kprime
moveq r0,#1 @ yes -> kprime
100:
pop {r1-r7,lr} @ restaur registers
bx lr @return
/******************************************************************/
/* display text with size calculation */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {r0,r1,r2,r7,lr} @ save registres
mov r2,#0 @ counter length
1: @ loop length calculation
ldrb r1,[r0,r2] @ read octet start position + index
cmp r1,#0 @ if 0 its over
addne r2,r2,#1 @ else add 1 in the length
bne 1b @ and loop
@ so here r2 contains the length of the message
mov r1,r0 @ address message in r1
mov r0,#STDOUT @ code to write to the standard output Linux
mov r7, #WRITE @ code call system "write"
svc #0 @ call systeme
pop {r0,r1,r2,r7,lr} @ restaur des 2 registres */
bx lr @ return
/******************************************************************/
/* Converting a register to a decimal unsigned */
/******************************************************************/
/* r0 contains value and r1 address area */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes */
.equ LGZONECAL, 10
conversion10:
push {r1-r4,lr} @ save registers
mov r3,r1
mov r2,#LGZONECAL
1: @ start loop
bl divisionpar10U @ unsigned r0 <- dividende. quotient ->r0 reste -> r1
add r1,#48 @ digit
strb r1,[r3,r2] @ store digit on area
cmp r0,#0 @ stop if quotient = 0
subne r2,#1 @ else previous position
bne 1b @ and loop
@ and move digit from left of area
mov r4,#0
2:
ldrb r1,[r3,r2]
strb r1,[r3,r4]
add r2,#1
add r4,#1
cmp r2,#LGZONECAL
ble 2b
@ and move spaces in end on area
mov r0,r4 @ result length
mov r1,#' ' @ space
3:
strb r1,[r3,r4] @ store space in area
add r4,#1 @ next position
cmp r4,#LGZONECAL
ble 3b @ loop if r4 <= area size
100:
pop {r1-r4,lr} @ restaur registres
bx lr @return
/***************************************************/
/* division par 10 unsigned */
/***************************************************/
/* r0 dividende */
/* r0 quotient */
/* r1 remainder */
divisionpar10U:
push {r2,r3,r4, lr}
mov r4,r0 @ save value
ldr r3,iMagicNumber @ r3 <- magic_number raspberry 1 2
umull r1, r2, r3, r0 @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0)
mov r0, r2, LSR #3 @ r2 <- r2 >> shift 3
add r2,r0,r0, lsl #2 @ r2 <- r0 * 5
sub r1,r4,r2, lsl #1 @ r1 <- r4 - (r2 * 2) = r4 - (r0 * 10)
pop {r2,r3,r4,lr}
bx lr @ leave function
iMagicNumber: .int 0xCCCCCCCD
/***************************************************/
/* integer division unsigned */
/***************************************************/
division:
/* r0 contains dividend */
/* r1 contains divisor */
/* r2 returns quotient */
/* r3 returns remainder */
push {r4, lr}
mov r2, #0 @ init quotient
mov r3, #0 @ init remainder
mov r4, #32 @ init counter bits
b 2f
1: @ loop
movs r0, r0, LSL #1 @ r0 <- r0 << 1 updating cpsr (sets C if 31st bit of r0 was 1)
adc r3, r3, r3 @ r3 <- r3 + r3 + C. This is equivalent to r3 ? (r3 << 1) + C
cmp r3, r1 @ compute r3 - r1 and update cpsr
subhs r3, r3, r1 @ if r3 >= r1 (C=1) then r3 <- r3 - r1
adc r2, r2, r2 @ r2 <- r2 + r2 + C. This is equivalent to r2 <- (r2 << 1) + C
2:
subs r4, r4, #1 @ r4 <- r4 - 1
bpl 1b @ if r4 >= 0 (N=0) then loop
pop {r4, lr}
bx lr

47
Task/Almost-prime/ASIC/almost-prime.asic Normal file
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REM Almost prime
FOR K = 1 TO 5
S$ = STR$(K)
S$ = LTRIM$(S$)
S$ = "k = " + S$
S$ = S$ + ":"
PRINT S$;
I = 2
C = 0
WHILE C < 10
AN = I
GOSUB CHECKKPRIME:
IF ISKPRIME <> 0 THEN
PRINT I;
C = C + 1
ENDIF
I = I + 1
WEND
PRINT
NEXT K
END
CHECKKPRIME:
REM Check if N (AN) is a K prime (result: ISKPRIME)
F = 0
J = 2
LOOPFOR:
ANMODJ = AN MOD J
LOOPWHILE:
IF ANMODJ <> 0 THEN AFTERWHILE:
IF F = K THEN FEQK:
F = F + 1
AN = AN / J
ANMODJ = AN MOD J
GOTO LOOPWHILE:
AFTERWHILE:
J = J + 1
IF J <= AN THEN LOOPFOR:
IF F = K THEN
ISKPRIME = -1
ELSE
ISKPRIME = 0
ENDIF
RETURN
FEQK:
ISKPRIME = 0
RETURN

25
Task/Almost-prime/AWK/almost-prime.awk Normal file
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# syntax: GAWK -f ALMOST_PRIME.AWK
BEGIN {
for (k=1; k<=5; k++) {
printf("%d:",k)
c = 0
i = 1
while (c < 10) {
if (kprime(++i,k)) {
printf(" %d",i)
c++
}
}
printf("\n")
}
exit(0)
}
function kprime(n,k, f,p) {
for (p=2; f<k && p*p<=n; p++) {
while (n % p == 0) {
n /= p
f++
}
}
return(f + (n > 1) == k)
}

39
Task/Almost-prime/Action-/almost-prime.action Normal file
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BYTE FUNC IsAlmostPrime(INT num BYTE k)
INT f,p,v
f=0 p=2 v=num
WHILE f<k AND p*p<=num
DO
WHILE v MOD p=0
DO
v==/p f==+1
OD
p==+1
OD
IF v>1 THEN
f==+1
FI
IF f=k THEN
RETURN (1)
FI
RETURN (0)
PROC Main()
BYTE count,k
INT i
FOR k=1 TO 5
DO
PrintF("k=%B:",k)
count=0 i=2
WHILE count<10
DO
IF IsAlmostPrime(i,k) THEN
PrintF(" %I",i)
count==+1
FI
i==+1
OD
PutE()
OD
RETURN

25
Task/Almost-prime/Ada/almost-prime.ada Normal file
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with Prime_Numbers, Ada.Text_IO;
procedure Test_Kth_Prime is
package Integer_Numbers is new
Prime_Numbers (Natural, 0, 1, 2);
use Integer_Numbers;
Out_Length: constant Positive := 10; -- 10 k-th almost primes
N: Positive; -- the "current number" to be checked
begin
for K in 1 .. 5 loop
Ada.Text_IO.Put("K =" & Integer'Image(K) &": ");
N := 2;
for I in 1 .. Out_Length loop
while Decompose(N)'Length /= K loop
N := N + 1;
end loop; -- now N is Kth almost prime;
Ada.Text_IO.Put(Integer'Image(Integer(N)));
N := N + 1;
end loop;
Ada.Text_IO.New_Line;
end loop;
end Test_Kth_Prime;

28
Task/Almost-prime/Arturo/almost-prime.arturo Normal file
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almostPrime: function [k, listLen][
result: new []
test: 2
c: 0
while [c < listLen][
i: 2
m: 0
n: test
while [i =< n][
if? zero? n % i [
n: n / i
m: m + 1
]
else -> i: i + 1
]
if m = k [
'result ++ test
c: c + 1
]
test: test + 1
]
return result
]
loop 1..5 'x ->
print ["k:" x "=>" almostPrime x 10]

27
Task/Almost-prime/AutoHotkey/almost-prime.ahk Normal file
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kprime(n,k) {
p:=2, f:=0
while( (f<k) && (p*p<=n) ) {
while ( 0==mod(n,p) ) {
n/=p
f++
}
p++
}
return f + (n>1) == k
}
k:=1, results:=""
while( k<=5 ) {
i:=2, c:=0, results:=results "k =" k ":"
while( c<10 ) {
if (kprime(i,k)) {
results:=results " " i
c++
}
i++
}
results:=results "`n"
k++
}
MsgBox % results

15
Task/Almost-prime/BASIC/almost-prime.basic Normal file
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10 DEFINT A-Z
20 FOR K=1 TO 5
30 PRINT USING "K = #:";K;
40 I=2: C=0
50 F=0: P=2: N=I
60 IF F >= K OR P*P > N THEN 100
70 IF N MOD P = 0 THEN N = N/P: F = F+1: GOTO 70
80 P = P+1
90 GOTO 60
100 IF N > 1 THEN F = F+1
110 IF F = K THEN C = C+1: PRINT USING " ###";I;
120 I = I+1
130 IF C < 10 THEN 50
140 PRINT
150 NEXT K

26
Task/Almost-prime/BASIC256/almost-prime.basic Normal file
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function kPrime(n, k)
f = 0
for i = 2 to n
while n mod i = 0
if f = k then return False
f += 1
n /= i
end while
next i
return f = k
end function
for k = 1 to 5
print "k = "; k; " :";
i = 2
c = 0
while c < 10
if kPrime(i, k) then
print rjust (string(i), 4);
c += 1
end if
i += 1
end while
print
next k
end

29
Task/Almost-prime/BCPL/almost-prime.bcpl Normal file
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get "libhdr"
let kprime(n, k) = valof
$( let f, p = 0, 2
while f<k & p*p<=n do
$( while n rem p = 0 do
$( n := n/p
f := f+1
$)
p := p+1
$)
if n > 1 then f := f + 1
resultis f = k
$)
let start() be
$( for k=1 to 5 do
$( let i, c = 2, 0
writef("k = %N:", k)
while c < 10 do
$( if kprime(i, k) then
$( writed(i, 4)
c := c+1
$)
i := i+1
$)
wrch('*N')
$)
$)

6
Task/Almost-prime/Befunge/almost-prime.bf Normal file
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1>::48*"= k",,,,02p.":",01v
|^ v0!`\*:g40:<p402p300:+1<
K| >2g03g`*#v_ 1`03g+02g->|
F@>/03g1+03p>vpv+1\.:,*48 <
P#|!\g40%g40:<4>:9`>#v_\1^|
|^>#!1#`+#50#:^#+1,+5>#5$<|

32
Task/Almost-prime/C++/almost-prime.cpp Normal file
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#include <cstdlib>
#include <iostream>
#include <sstream>
#include <iomanip>
#include <list>
bool k_prime(unsigned n, unsigned k) {
unsigned f = 0;
for (unsigned p = 2; f < k && p * p <= n; p++)
while (0 == n % p) { n /= p; f++; }
return f + (n > 1 ? 1 : 0) == k;
}
std::list<unsigned> primes(unsigned k, unsigned n) {
std::list<unsigned> list;
for (unsigned i = 2;list.size() < n;i++)
if (k_prime(i, k)) list.push_back(i);
return list;
}
int main(const int argc, const char* argv[]) {
using namespace std;
for (unsigned k = 1; k <= 5; k++) {
ostringstream os("");
const list<unsigned> l = primes(k, 10);
for (list<unsigned>::const_iterator i = l.begin(); i != l.end(); i++)
os << setw(4) << *i;
cout << "k = " << k << ':' << os.str() << endl;
}
return EXIT_SUCCESS;
}

55
Task/Almost-prime/C-sharp/almost-prime.cs Normal file
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using System;
using System.Collections.Generic;
using System.Linq;
namespace AlmostPrime
{
class Program
{
static void Main(string[] args)
{
foreach (int k in Enumerable.Range(1, 5))
{
KPrime kprime = new KPrime() { K = k };
Console.WriteLine("k = {0}: {1}",
k, string.Join<int>(" ", kprime.GetFirstN(10)));
}
}
}
class KPrime
{
public int K { get; set; }
public bool IsKPrime(int number)
{
int primes = 0;
for (int p = 2; p * p <= number && primes < K; ++p)
{
while (number % p == 0 && primes < K)
{
number /= p;
++primes;
}
}
if (number > 1)
{
++primes;
}
return primes == K;
}
public List<int> GetFirstN(int n)
{
List<int> result = new List<int>();
for (int number = 2; result.Count < n; ++number)
{
if (IsKPrime(number))
{
result.Add(number);
}
}
return result;
}
}
}

30
Task/Almost-prime/C/almost-prime.c Normal file
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#include <stdio.h>
int kprime(int n, int k)
{
int p, f = 0;
for (p = 2; f < k && p*p <= n; p++)
while (0 == n % p)
n /= p, f++;
return f + (n > 1) == k;
}
int main(void)
{
int i, c, k;
for (k = 1; k <= 5; k++) {
printf("k = %d:", k);
for (i = 2, c = 0; c < 10; i++)
if (kprime(i, k)) {
printf(" %d", i);
c++;
}
putchar('\n');
}
return 0;
}

30
Task/Almost-prime/CLU/almost-prime.clu Normal file
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kprime = proc (n,k: int) returns (bool)
f: int := 0
p: int := 2
while f<k & p*p<=n do
while n//p=0 do
n := n/p
f := f+1
end
p := p+1
end
if n>1 then f:=f+1 end
return(f=k)
end kprime
start_up = proc ()
po: stream := stream$primary_output()
for k: int in int$from_to(1,5) do
i: int := 2
c: int := 0
stream$puts(po, "k = " || int$unparse(k) || ":")
while c<10 do
if kprime(i,k) then
stream$putright(po, int$unparse(i), 4)
c := c+1
end
i := i+1
end
stream$putl(po, "")
end
end start_up

69
Task/Almost-prime/COBOL/almost-prime.cobol Normal file
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IDENTIFICATION DIVISION.
PROGRAM-ID. ALMOST-PRIME.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 CONTROL-VARS.
03 K PIC 9.
03 I PIC 999.
03 SEEN PIC 99.
03 N PIC 999.
03 P PIC 99.
03 P-SQUARED PIC 9(4).
03 F PIC 99.
03 N-DIV-P PIC 999V999.
03 FILLER REDEFINES N-DIV-P.
05 NEXT-N PIC 999.
05 FILLER PIC 999.
88 N-DIVS-P VALUE ZERO.
01 OUT-VARS.
03 K-LN PIC X(70).
03 K-LN-PTR PIC 99.
03 LN-HDR.
05 FILLER PIC X(4) VALUE "K = ".
05 K-OUT PIC 9.
05 FILLER PIC X VALUE ":".
03 I-FMT.
05 FILLER PIC X VALUE SPACE.
05 I-OUT PIC ZZ9.
PROCEDURE DIVISION.
BEGIN.
PERFORM K-ALMOST-PRIMES VARYING K FROM 1 BY 1
UNTIL K IS GREATER THAN 5.
STOP RUN.
K-ALMOST-PRIMES.
MOVE SPACES TO K-LN.
MOVE 1 TO K-LN-PTR.
MOVE ZERO TO SEEN.
MOVE K TO K-OUT.
STRING LN-HDR DELIMITED BY SIZE INTO K-LN
WITH POINTER K-LN-PTR.
PERFORM I-K-ALMOST-PRIME VARYING I FROM 2 BY 1
UNTIL SEEN IS EQUAL TO 10.
DISPLAY K-LN.
I-K-ALMOST-PRIME.
MOVE ZERO TO F, P-SQUARED.
MOVE I TO N.
PERFORM PRIME-FACTOR VARYING P FROM 2 BY 1
UNTIL F IS NOT LESS THAN K
OR P-SQUARED IS GREATER THAN N.
IF N IS GREATER THAN 1, ADD 1 TO F.
IF F IS EQUAL TO K,
MOVE I TO I-OUT,
ADD 1 TO SEEN,
STRING I-FMT DELIMITED BY SIZE INTO K-LN
WITH POINTER K-LN-PTR.
PRIME-FACTOR.
MULTIPLY P BY P GIVING P-SQUARED.
DIVIDE N BY P GIVING N-DIV-P.
PERFORM DIVIDE-FACTOR UNTIL NOT N-DIVS-P.
DIVIDE-FACTOR.
MOVE NEXT-N TO N.
ADD 1 TO F.
DIVIDE N BY P GIVING N-DIV-P.

24
Task/Almost-prime/Chipmunk-Basic/almost-prime.basic Normal file
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10 'Almost prime
20 FOR k = 1 TO 5
30 PRINT "k = "; k; ":";
40 LET i = 2
50 LET c = 0
60 WHILE c < 10
70 LET an = i: GOSUB 150
80 IF iskprime <> 0 THEN PRINT USING " ###"; i; : LET c = c + 1
90 LET i = i + 1
100 WEND
110 PRINT
120 NEXT k
130 END
140 ' Check if n (AN) is a k (K) prime
150 LET f = 0
160 FOR j = 2 TO an
170 WHILE an MOD j = 0
180 IF f = k THEN LET iskprime = 0: RETURN
190 LET f = f + 1
200 LET an = INT(an / j)
210 WEND
220 NEXT j
230 LET iskprime = (f = k)
240 RETURN

23
Task/Almost-prime/Clojure/almost-prime.clj Normal file
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(ns clojure.examples.almostprime
(:gen-class))
(defn divisors [n]
" Finds divisors by looping through integers 2, 3,...i.. up to sqrt (n) [note: rather than compute sqrt(), test with i*i <=n] "
(let [div (some #(if (= 0 (mod n %)) % nil) (take-while #(<= (* % %) n) (iterate inc 2)))]
(if div ; div = nil (if no divisor found else its the divisor)
(into [] (concat (divisors div) (divisors (/ n div)))) ; Concat the two divisors of the two divisors
[n]))) ; Number is prime so only itself as a divisor
(defn divisors-k [k n]
" Finds n numbers with k divisors. Does this by looping through integers 2, 3, ... filtering (passing) ones with k divisors and
taking the first n "
(->> (iterate inc 2) ; infinite sequence of numbers starting at 2
(map divisors) ; compute divisor of each element of sequence
(filter #(= (count %) k)) ; filter to take only elements with k divisors
(take n) ; take n elements from filtered sequence
(map #(apply * %)))) ; compute number by taking product of divisors
(println (for [k (range 1 6)]
(println "k:" k (divisors-k k 10))))
}

13
Task/Almost-prime/Common-Lisp/almost-prime.lisp Normal file
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(defun start ()
(loop for k from 1 to 5
do (format t "k = ~a: ~a~%" k (collect-k-almost-prime k))))
(defun collect-k-almost-prime (k &optional (d 2) (lst nil))
(cond ((= (length lst) 10) (reverse lst))
((= (?-primality d) k) (collect-k-almost-prime k (+ d 1) (cons d lst)))
(t (collect-k-almost-prime k (+ d 1) lst))))
(defun ?-primality (n &optional (d 2) (c 0))
(cond ((> d (isqrt n)) (+ c 1))
((zerop (rem n d)) (?-primality (/ n d) d (+ c 1)))
(t (?-primality n (+ d 1) c))))

41
Task/Almost-prime/Cowgol/almost-prime.cowgol Normal file
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include "cowgol.coh";
sub kprime(n: uint8, k: uint8): (kp: uint8) is
var p: uint8 := 2;
var f: uint8 := 0;
while f < k and p*p <= n loop
while 0 == n % p loop
n := n / p;
f := f + 1;
end loop;
p := p + 1;
end loop;
if n > 1 then
f := f + 1;
end if;
if f == k then
kp := 1;
else
kp := 0;
end if;
end sub;
var k: uint8 := 1;
while k <= 5 loop
print("k = ");
print_i8(k);
print(":");
var i: uint8 := 2;
var c: uint8 := 0;
while c < 10 loop
if kprime(i,k) != 0 then
print(" ");
print_i8(i);
c := c + 1;
end if;
i := i + 1;
end loop;
print_nl();
k := k + 1;
end loop;

36
Task/Almost-prime/D/almost-prime.d Normal file
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import std.stdio, std.algorithm, std.traits;
Unqual!T[] decompose(T)(in T number) pure nothrow
in {
assert(number > 1);
} body {
typeof(return) result;
Unqual!T n = number;
for (Unqual!T i = 2; n % i == 0; n /= i)
result ~= i;
for (Unqual!T i = 3; n >= i * i; i += 2)
for (; n % i == 0; n /= i)
result ~= i;
if (n != 1)
result ~= n;
return result;
}
void main() {
enum outLength = 10; // 10 k-th almost primes.
foreach (immutable k; 1 .. 6) {
writef("K = %d: ", k);
auto n = 2; // The "current number" to be checked.
foreach (immutable i; 1 .. outLength + 1) {
while (n.decompose.length != k)
n++;
// Now n is K-th almost prime.
write(n, " ");
n++;
}
writeln;
}
}

40
Task/Almost-prime/Delphi/almost-prime.delphi Normal file
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program AlmostPrime;
{$APPTYPE CONSOLE}
function IsKPrime(const n, k: Integer): Boolean;
var
p, f, v: Integer;
begin
f := 0;
p := 2;
v := n;
while (f < k) and (p*p <= n) do begin
while (v mod p) = 0 do begin
v := v div p;
Inc(f);
end;
Inc(p);
end;
if v > 1 then Inc(f);
Result := f = k;
end;
var
i, c, k: Integer;
begin
for k := 1 to 5 do begin
Write('k = ', k, ':');
c := 0;
i := 2;
while c < 10 do begin
if IsKPrime(i, k) then begin
Write(' ', i);
Inc(c);
end;
Inc(i);
end;
WriteLn;
end;
end.

32
Task/Almost-prime/Draco/almost-prime.draco Normal file
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proc nonrec kprime(word n, k) bool:
word f, p;
f := 0;
p := 2;
while f < k and p*p <= n do
while n%p = 0 do
n := n/p;
f := f+1
od;
p := p+1
od;
if n>1 then f+1 = k
else f = k
fi
corp
proc nonrec main() void:
byte k, i, c;
for k from 1 upto 5 do
write("k = ", k:1, ":");
i := 2;
c := 0;
while c < 10 do
if kprime(i,k) then
write(i:4);
c := c+1
fi;
i := i+1
od;
writeln()
od
corp

36
Task/Almost-prime/ERRE/almost-prime.erre Normal file
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PROGRAM ALMOST_PRIME
!
! for rosettacode.org
!
!$INTEGER
PROCEDURE KPRIME(N,K->KP)
LOCAL P,F
FOR P=2 TO 999 DO
EXIT IF NOT((F<K) AND (P*P<=N))
WHILE (N MOD P)=0 DO
N/=P
F+=1
END WHILE
END FOR
KP=(F-(N>1)=K)
END PROCEDURE
BEGIN
PRINT(CHR$(12);) !CLS
FOR K=1 TO 5 DO
PRINT("k =";K;":";)
C=0
FOR I=2 TO 999 DO
EXIT IF NOT(C<10)
KPRIME(I,K->KP)
IF KP THEN
PRINT(I;)
C+=1
END IF
END FOR
PRINT
END FOR
END PROGRAM

11
Task/Almost-prime/EchoLisp/almost-prime-1.l Normal file
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(define (almost-prime? p k)
(= k (length (prime-factors p))))
(define (almost-primes k nmax)
(take (filter (rcurry almost-prime? k) [2 ..]) nmax))
(define (task (kmax 6) (nmax 10))
(for ((k [1 .. kmax]))
(write 'k= k '|)
(for-each write (almost-primes k nmax))
(writeln)))

7
Task/Almost-prime/EchoLisp/almost-prime-2.l Normal file
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(task)
k= 1 | 2 3 5 7 11 13 17 19 23 29
k= 2 | 4 6 9 10 14 15 21 22 25 26
k= 3 | 8 12 18 20 27 28 30 42 44 45
k= 4 | 16 24 36 40 54 56 60 81 84 88
k= 5 | 32 48 72 80 108 112 120 162 168 176

50
Task/Almost-prime/EchoLisp/almost-prime-3.l Normal file
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(lib 'match)
(define-syntax-rule (: v i) (vector-ref v i))
(reader-infix ':) ;; abbrev (vector-ref v i) === [v : i]
(lib 'bigint)
(define cprimes (list->vector (primes 10000)))
;; generates next k-almost-prime < pmax
;; c = vector of k primes indices c[i] <= c[j]
;; p = vector of intermediate products prime[c[0]]*prime[c[1]]*..
;; p[k-1] is the generated k-almost-prime
;; increment one c[i] at each step
(define (almost-next pmax k c p)
(define almost-prime #f)
(define cp 0)
(for ((i (in-range (1- k) -1 -1))) ;; look backwards for c[i] to increment
(vector-set! c i (1+ [c : i])) ;; increment c[i]
(set! cp [cprimes : [c : i]])
(vector-set! p i (if (> i 0) (* [ p : (1- i)] cp) cp)) ;; update partial product
(when (< [p : i) pmax)
(set! almost-prime
(and ;; set followers to c[i] value
(for ((j (in-range (1+ i) k)))
(vector-set! c j [c : i])
(vector-set! p j (* [ p : (1- j)] cp))
#:break (>= [p : j] pmax) => #f )
[p : (1- k)]
) ;; // and
) ;; set!
) ;; when
#:break almost-prime
) ;; // for i
almost-prime )
;; not sorted list of k-almost-primes < pmax
(define (almost-primes k nmax)
(define base (expt 2 k)) ;; first one is 2^k
(define pmax (* base nmax))
(define c (make-vector k #0))
(define p (build-vector k (lambda(i) (expt #2 (1+ i)))))
(cons base
(for/list
((almost-prime (in-producer almost-next pmax k c p )))
almost-prime)))

8
Task/Almost-prime/EchoLisp/almost-prime-4.l Normal file
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;; we want 500-almost-primes from the 10000-th.
(take (drop (list-sort < (almost-primes 500 10000)) 10000 ) 10)
(7241149198492252834202927258094752774597239286103014697435725917649659974371690699721153852986
440733637405206125678822081264723636566725108094369093648384
etc ...
;; The first one is 2^497 * 3 * 17 * 347 , same result as Haskell.

23
Task/Almost-prime/Elixir/almost-prime.elixir Normal file
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defmodule Factors do
def factors(n), do: factors(n,2,[])
defp factors(1,_,acc), do: acc
defp factors(n,k,acc) when rem(n,k)==0, do: factors(div(n,k),k,[k|acc])
defp factors(n,k,acc) , do: factors(n,k+1,acc)
def kfactors(n,k), do: kfactors(n,k,1,1,[])
defp kfactors(_tn,tk,_n,k,_acc) when k == tk+1, do: IO.puts "done! "
defp kfactors(tn,tk,_n,k,acc) when length(acc) == tn do
IO.puts "K: #{k} #{inspect acc}"
kfactors(tn,tk,2,k+1,[])
end
defp kfactors(tn,tk,n,k,acc) do
case length(factors(n)) do
^k -> kfactors(tn,tk,n+1,k,acc++[n])
_ -> kfactors(tn,tk,n+1,k,acc)
end
end
end
Factors.kfactors(10,5)

24
Task/Almost-prime/Erlang/almost-prime.erl Normal file
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-module(factors).
-export([factors/1,kfactors/0,kfactors/2]).
factors(N) ->
factors(N,2,[]).
factors(1,_,Acc) -> Acc;
factors(N,K,Acc) when N rem K == 0 ->
factors(N div K,K, [K|Acc]);
factors(N,K,Acc) ->
factors(N,K+1,Acc).
kfactors() -> kfactors(10,5,1,1,[]).
kfactors(N,K) -> kfactors(N,K,1,1,[]).
kfactors(_Tn,Tk,_N,K,_Acc) when K == Tk+1 -> io:fwrite("Done! ");
kfactors(Tn,Tk,N,K,Acc) when length(Acc) == Tn ->
io:format("K: ~w ~w ~n", [K, Acc]),
kfactors(Tn,Tk,2,K+1,[]);
kfactors(Tn,Tk,N,K,Acc) ->
case length(factors(N)) of K ->
kfactors(Tn,Tk, N+1,K, Acc ++ [ N ] );
_ ->
kfactors(Tn,Tk, N+1,K, Acc) end.

19
Task/Almost-prime/F-Sharp/almost-prime.fs Normal file
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let rec genFactor (f, n) =
if f > n then None
elif n % f = 0 then Some (f, (f, n/f))
else genFactor (f+1, n)
let factorsOf (num) =
Seq.unfold (fun (f, n) -> genFactor (f, n)) (2, num)
let kFactors k = Seq.unfold (fun n ->
let rec loop m =
if Seq.length (factorsOf m) = k then m
else loop (m+1)
let next = loop n
Some(next, next+1)) 2
[1 .. 5]
|> List.iter (fun k ->
printfn "%A" (Seq.take 10 (kFactors k) |> Seq.toList))

20
Task/Almost-prime/FOCAL/almost-prime.focal Normal file
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01.10 F K=1,5;D 3
01.20 Q
02.10 S N=I;S P=1;S G=0
02.20 S P=P+1
02.30 I (K-G)2.7,2.7;I (N-P*P)2.7
02.40 S Z=FITR(N/P)
02.50 I (Z*P-N)2.2
02.60 S N=Z;S G=G+1;G 2.4
02.70 I (1-N)2.8;R
02.80 S G=G+1
03.10 T "K",%1,K,":"
03.20 S I=2;S C=0
03.30 D 2;I (G-K)3.6,3.4,3.6
03.40 T " ",%3,I
03.50 S C=C+1
03.60 S I=I+1
03.70 I (C-10)3.3
03.80 T !

12
Task/Almost-prime/Factor/almost-prime.factor Normal file
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USING: formatting fry kernel lists lists.lazy locals
math.combinatorics math.primes.factors math.ranges sequences ;
IN: rosetta-code.almost-prime
: k-almost-prime? ( n k -- ? )
'[ factors _ <combinations> [ product ] map ]
[ [ = ] curry ] bi any? ;
:: first10 ( k -- seq )
10 0 lfrom [ k k-almost-prime? ] lfilter ltake list>array ;
5 [1,b] [ dup first10 "K = %d: %[%3d, %]\n" printf ] each

45
Task/Almost-prime/Fortran/almost-prime.f Normal file
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program almost_prime
use iso_fortran_env, only: output_unit
implicit none
integer :: i, c, k
do k = 1, 5
write(output_unit,'(A3,x,I0,x,A1,x)', advance="no") "k =", k, ":"
i = 2
c = 0
do
if (c >= 10) exit
if (kprime(i, k)) then
write(output_unit,'(I0,x)', advance="no") i
c = c + 1
end if
i = i + 1
end do
write(output_unit,*)
end do
contains
pure function kprime(n, k)
integer, intent(in) :: n, k
logical :: kprime
integer :: p, f, i
kprime = .false.
f = 0
i = n
do p = 2, n
do
if (modulo(i, p) /= 0) exit
if (f == k) return
f = f + 1
i = i / p
end do
end do
kprime = f==k
end function kprime
end program almost_prime

32
Task/Almost-prime/FreeBASIC/almost-prime.basic Normal file
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' FB 1.05.0 Win64
Function kPrime(n As Integer, k As Integer) As Boolean
Dim f As Integer = 0
For i As Integer = 2 To n
While n Mod i = 0
If f = k Then Return false
f += 1
n \= i
Wend
Next
Return f = k
End Function
Dim As Integer i, c, k
For k = 1 To 5
Print "k = "; k; " : ";
i = 2
c = 0
While c < 10
If kPrime(i, k) Then
Print Using "### "; i;
c += 1
End If
i += 1
Wend
Print
Next
Print
Print "Press any key to quit"
Sleep

17
Task/Almost-prime/Frink/almost-prime.frink Normal file
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for k = 1 to 5
{
n=2
count = 0
print["k=$k:"]
do
{
if length[factorFlat[n]] == k
{
print[" $n"]
count = count + 1
}
n = n + 1
} while count < 10
println[]
}

18
Task/Almost-prime/Futhark/almost-prime.futhark Normal file
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let kprime(n: i32, k: i32): bool =
let (p,f) = (2, 0)
let (n,_,f) = loop (n, p, f) while f < k && p*p <= n do
let (n,f) = loop (n, f) while 0 == n % p do
(n/p, f+1)
in (n, p+1, f)
in f + (if n > 1 then 1 else 0) == k
let main(m: i32): [][]i32 =
let f k =
let ps = replicate 10 0
let (_,_,ps) = loop (i,c,ps) = (2,0,ps) while c < 10 do
if kprime(i,k) then
unsafe let ps[c] = i
in (i+1, c+1, ps)
else (i+1, c, ps)
in ps
in map f (1...m)

25
Task/Almost-prime/GW-BASIC/almost-prime.basic Normal file
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10 'Almost prime
20 FOR K% = 1 TO 5
30 PRINT "k = "; K%; ":";
40 LET I% = 2
50 LET C% = 0
60 WHILE C% < 10
70 LET AN% = I%: GOSUB 1000
80 IF ISKPRIME <> 0 THEN PRINT USING " ###"; I%;: LET C% = C% + 1
90 LET I% = I% + 1
100 WEND
110 PRINT
120 NEXT K%
130 END
995 ' Check if n (AN%) is a k (K%) prime
1000 LET F% = 0
1010 FOR J% = 2 TO AN%
1020 WHILE AN% MOD J% = 0
1030 IF F% = K% THEN LET ISKPRIME = 0: RETURN
1040 LET F% = F% + 1
1050 LET AN% = AN% \ J%
1060 WEND
1070 NEXT J%
1080 LET ISKPRIME = (F% = K%)
1090 RETURN

36
Task/Almost-prime/Go/almost-prime.go Normal file
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package main
import "fmt"
func kPrime(n, k int) bool {
nf := 0
for i := 2; i <= n; i++ {
for n%i == 0 {
if nf == k {
return false
}
nf++
n /= i
}
}
return nf == k
}
func gen(k, n int) []int {
r := make([]int, n)
n = 2
for i := range r {
for !kPrime(n, k) {
n++
}
r[i] = n
n++
}
return r
}
func main() {
for k := 1; k <= 5; k++ {
fmt.Println(k, gen(k, 10))
}
}

34
Task/Almost-prime/Groovy/almost-prime.groovy Normal file
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public class almostprime
{
public static boolean kprime(int n,int k)
{
int i,div=0;
for(i=2;(i*i <= n) && (div<k);i++)
{
while(n%i==0)
{
n = n/i;
div++;
}
}
return div + ((n > 1)?1:0) == k;
}
public static void main(String[] args)
{
int i,l,k;
for(k=1;k<=5;k++)
{
println("k = " + k + ":");
l = 0;
for(i=2;l<10;i++)
{
if(kprime(i,k))
{
print(i + " ");
l++;
}
}
println();
}
}
}​

18
Task/Almost-prime/Haskell/almost-prime-1.hs Normal file
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isPrime :: Integral a => a -> Bool
isPrime n = not $ any ((0 ==) . (mod n)) [2..(truncate $ sqrt $ fromIntegral n)]
primes :: [Integer]
primes = filter isPrime [2..]
isKPrime :: (Num a, Eq a) => a -> Integer -> Bool
isKPrime 1 n = isPrime n
isKPrime k n = any (isKPrime (k - 1)) sprimes
where
sprimes = map fst $ filter ((0 ==) . snd) $ map (divMod n) $ takeWhile (< n) primes
kPrimes :: (Num a, Eq a) => a -> [Integer]
kPrimes k = filter (isKPrime k) [2..]
main :: IO ()
main = flip mapM_ [1..5] $ \k ->
putStrLn $ "k = " ++ show k ++ ": " ++ (unwords $ map show (take 10 $ kPrimes k))

27
Task/Almost-prime/Haskell/almost-prime-2.hs Normal file
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primes = 2:3:[n | n <- [5,7..], foldr (\p r-> p*p > n || rem n p > 0 && r)
True (drop 1 primes)]
merge aa@(a:as) bb@(b:bs)
| a < b = a:merge as bb
| otherwise = b:merge aa bs
-- n-th item is all k-primes not divisible by any of the first n primes
notdivs k = f primes $ kprimes (k-1) where
f (p:ps) s = map (p*) s : f ps (filter ((/=0).(`mod`p)) s)
kprimes k
| k == 1 = primes
| otherwise = f (head ndk) (tail ndk) (tail $ map (^k) primes) where
ndk = notdivs k
-- tt is the thresholds for merging in next sequence
-- it is equal to "map head seqs", but don't do that
f aa@(a:as) seqs tt@(t:ts)
| a < t = a : f as seqs tt
| otherwise = f (merge aa $ head seqs) (tail seqs) ts
main = do
-- next line is for task requirement:
mapM_ (\x->print (x, take 10 $ kprimes x)) [1 .. 5]
putStrLn "\n10000th to 10100th 500-amost primes:"
mapM_ print $ take 100 $ drop 10000 $ kprimes 500

10
Task/Almost-prime/Icon/almost-prime.icon Normal file
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link "factors"
procedure main()
every writes(k := 1 to 5,": ") do
every writes(right(genKap(k),5)\10|"\n")
end
procedure genKap(k)
suspend (k = *factors(n := seq(q)), n)
end

6
Task/Almost-prime/J/almost-prime.j Normal file
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@ -0,0 +1,6 @@
(10 {. [:~.[:/:~[:,*/~)^:(i.5)~p:i.10
2 3 5 7 11 13 17 19 23 29
4 6 9 10 14 15 21 22 25 26
8 12 18 20 27 28 30 42 44 45
16 24 36 40 54 56 60 81 84 88
32 48 72 80 108 112 120 162 168 176

27
Task/Almost-prime/Java/almost-prime.java Normal file
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@ -0,0 +1,27 @@
public class AlmostPrime {
public static void main(String[] args) {
for (int k = 1; k <= 5; k++) {
System.out.print("k = " + k + ":");
for (int i = 2, c = 0; c < 10; i++) {
if (kprime(i, k)) {
System.out.print(" " + i);
c++;
}
}
System.out.println("");
}
}
public static boolean kprime(int n, int k) {
int f = 0;
for (int p = 2; f < k && p * p <= n; p++) {
while (n % p == 0) {
n /= p;
f++;
}
}
return f + ((n > 1) ? 1 : 0) == k;
}
}

24
Task/Almost-prime/JavaScript/almost-prime.js Normal file
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@ -0,0 +1,24 @@
function almostPrime (n, k) {
var divisor = 2, count = 0
while(count < k + 1 && n != 1) {
if (n % divisor == 0) {
n = n / divisor
count = count + 1
} else {
divisor++
}
}
return count == k
}
for (var k = 1; k <= 5; k++) {
document.write("<br>k=", k, ": ")
var count = 0, n = 0
while (count <= 10) {
n++
if (almostPrime(n, k)) {
document.write(n, " ")
count++
}
}
}

84
Task/Almost-prime/Jq/almost-prime-1.jq Normal file
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# Recent versions of jq (version > 1.4) have the following definition of "until":
def until(cond; next):
def _until:
if cond then . else (next|_until) end;
_until;
# relatively_prime(previous) tests whether the input integer is prime
# relative to the primes in the array "previous":
def relatively_prime(previous):
. as $in
| (previous|length) as $plen
# state: [found, ix]
| [false, 0]
| until( .[0] or .[1] >= $plen;
[ ($in % previous[.[1]]) == 0, .[1] + 1] )
| .[0] | not ;
# Emit a stream in increasing order of all primes (from 2 onwards)
# that are less than or equal to mx:
def primes(mx):
# The helper function, next, has arity 0 for tail recursion optimization;
# it expects its input to be the array of previously found primes:
def next:
. as $previous
| ($previous | .[length-1]) as $last
| if ($last >= mx) then empty
else ((2 + $last)
| until( relatively_prime($previous) ; . + 2)) as $nextp
| if $nextp <= mx
then $nextp, (( $previous + [$nextp] ) | next)
else empty
end
end;
if mx <= 1 then empty
elif mx == 2 then 2
else (2, 3, ( [2,3] | next))
end
;
# Return an array of the distinct prime factors of . in increasing order
def prime_factors:
# Return an array of prime factors of . given that "primes"
# is an array of relevant primes:
def pf(primes):
if . <= 1 then []
else . as $in
| if ($in | relatively_prime(primes)) then [$in]
else reduce primes[] as $p
([];
if ($in % $p) != 0 then .
else . + [$p] + (($in / $p) | pf(primes))
end)
end
| unique
end;
if . <= 1 then []
else . as $in
| pf( [ primes( (1+$in) | sqrt | floor) ] )
end;
# Return an array of prime factors of . repeated according to their multiplicities:
def prime_factors_with_multiplicities:
# Emit p according to the multiplicity of p
# in the input integer assuming p > 1
def multiplicity(p):
if . < p then empty
elif . == p then p
elif (. % p) == 0 then
((./p) | recurse( if (. % p) == 0 then (. / p) else empty end) | p)
else empty
end;
if . <= 1 then []
else . as $in
| prime_factors as $primes
| if ($in|relatively_prime($primes)) then [$in]
else reduce $primes[] as $p
([];
if ($in % $p) == 0 then . + [$in|multiplicity($p)] else . end )
end
end;

14
Task/Almost-prime/Jq/almost-prime-2.jq Normal file
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def isalmostprime(k): (prime_factors_with_multiplicities | length) == k;
# Emit a stream of the first N almost-k primes
def almostprimes(N; k):
if N <= 0 then empty
else
# state [remaining, candidate, answer]
[N, 1, null]
| recurse( if .[0] <= 0 then empty
elif (.[1] | isalmostprime(k)) then [.[0]-1, .[1]+1, .[1]]
else [.[0], .[1]+1, null]
end)
| .[2] | select(. != null)
end;

1
Task/Almost-prime/Jq/almost-prime-3.jq Normal file
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@ -0,0 +1 @@
range(1;6) as $k | "k=\($k): \([almostprimes(10;$k)])"

6
Task/Almost-prime/Jq/almost-prime-4.jq Normal file
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@ -0,0 +1,6 @@
$ jq -c -r -n -f Almost_prime.jq
k=1: [2,3,5,7,11,13,17,19,23,29]
k=2: [4,6,9,10,14,15,21,22,25,26]
k=3: [8,12,18,20,27,28,30,42,44,45]
k=4: [16,24,36,40,54,56,60,81,84,88]
k=5: [32,48,72,80,108,112,120,162,168,176]

17
Task/Almost-prime/Julia/almost-prime.julia Normal file
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@ -0,0 +1,17 @@
using Primes
isalmostprime(n::Integer, k::Integer) = sum(values(factor(n))) == k
function almostprimes(N::Integer, k::Integer) # return first N almost-k primes
P = Vector{typeof(k)}(undef,N)
i = 0; n = 2
while i < N
if isalmostprime(n, k) P[i += 1] = n end
n += 1
end
return P
end
for k in 1:5
println("$k-Almost-primes: ", join(almostprimes(10, k), ", "), "...")
end

25
Task/Almost-prime/Kotlin/almost-prime.kotlin Normal file
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@ -0,0 +1,25 @@
fun Int.k_prime(x: Int): Boolean {
var n = x
var f = 0
var p = 2
while (f < this && p * p <= n) {
while (0 == n % p) { n /= p; f++ }
p++
}
return f + (if (n > 1) 1 else 0) == this
}
fun Int.primes(n : Int) : List<Int> {
var i = 2
var list = mutableListOf<Int>()
while (list.size < n) {
if (k_prime(i)) list.add(i)
i++
}
return list
}
fun main(args: Array<String>) {
for (k in 1..5)
println("k = $k: " + k.primes(10))
}

27
Task/Almost-prime/Liberty-BASIC/almost-prime.basic Normal file
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@ -0,0 +1,27 @@
' Almost prime
for k = 1 to 5
print "k = "; k; ":";
i = 2
c = 0
while c < 10
if kPrime(i, k) then
print " "; using("###", i);
c = c + 1
end if
i = i + 1
wend
print
next k
end
function kPrime(n, k)
f = 0
for i = 2 to n
while n mod i = 0
if f = k then kPrime = 0: exit function
f = f + 1
n = int(n / i)
wend
next i
kPrime = abs(f = k)
end function

34
Task/Almost-prime/Lua/almost-prime.lua Normal file
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-- Returns boolean indicating whether n is k-almost prime
function almostPrime (n, k)
local divisor, count = 2, 0
while count < k + 1 and n ~= 1 do
if n % divisor == 0 then
n = n / divisor
count = count + 1
else
divisor = divisor + 1
end
end
return count == k
end
-- Generates table containing first ten k-almost primes for given k
function kList (k)
local n, kTab = 2^k, {}
while #kTab < 10 do
if almostPrime(n, k) then
table.insert(kTab, n)
end
n = n + 1
end
return kTab
end
-- Main procedure, displays results from five calls to kList()
for k = 1, 5 do
io.write("k=" .. k .. ": ")
for _, v in pairs(kList(k)) do
io.write(v .. ", ")
end
print("...")
end

36
Task/Almost-prime/MAD/almost-prime.mad Normal file
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@ -0,0 +1,36 @@
NORMAL MODE IS INTEGER
INTERNAL FUNCTION(NN,KK)
ENTRY TO KPRIME.
F = 0
N = NN
THROUGH SCAN, FOR P=2, 1, F.GE.KK .OR. P*P.G.N
DIV WHENEVER N.E.N/P*P
N = N/P
F = F+1
TRANSFER TO DIV
END OF CONDITIONAL
SCAN CONTINUE
WHENEVER N.G.1, F = F+1
FUNCTION RETURN F.E.KK
END OF FUNCTION
VECTOR VALUES KFMT = $5(S1,2HK=,I1,S1)*$
VECTOR VALUES PFMT = $5(I4,S1)*$
PRINT FORMAT KFMT, 1, 2, 3, 4, 5
DIMENSION KPR(50)
THROUGH FNDKPR, FOR K=1, 1, K.G.5
C=0
THROUGH FNDKPR, FOR I=2, 1, C.GE.10
WHENEVER KPRIME.(I,K)
KPR(C*5+K) = I
C = C+1
END OF CONDITIONAL
FNDKPR CONTINUE
THROUGH OUT, FOR C=0, 1, C.GE.10
OUT PRINT FORMAT PFMT, KPR(C*5+1), KPR(C*5+2), KPR(C*5+3),
0 KPR(C*5+4), KPR(C*5+5)
END OF PROGRAM

16
Task/Almost-prime/Maple/almost-prime.maple Normal file
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@ -0,0 +1,16 @@
AlmostPrimes:=proc(k, numvalues::posint:=10)
local aprimes, i, intfactors;
aprimes := Array([]);
i := 0;
do
i := i + 1;
intfactors := ifactors(i)[2];
intfactors := [seq(seq(intfactors[i][1], j=1..intfactors[i][2]),i = 1..numelems(intfactors))];
if numelems(intfactors) = k then
ArrayTools:-Append(aprimes,i);
end if;
until numelems(aprimes) = 10:
aprimes;
end proc:
<seq( AlmostPrimes(i), i = 1..5 )>;

14
Task/Almost-prime/Mathematica/almost-prime.math Normal file
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@ -0,0 +1,14 @@
kprimes[k_,n_] :=
(* generates a list of the n smallest k-almost-primes *)
Module[{firstnprimes, runningkprimes = {}},
firstnprimes = Prime[Range[n]];
runningkprimes = firstnprimes;
Do[
runningkprimes =
Outer[Times, firstnprimes , runningkprimes ] // Flatten // Union // Take[#, n] & ;
(* only keep lowest n numbers in our running list *)
, {i, 1, k - 1}];
runningkprimes
]
(* now to create table with n=10 and k ranging from 1 to 5 *)
Table[Flatten[{"k = " <> ToString[i] <> ": ", kprimes[i, 10]}], {i,1,5}] // TableForm

46
Task/Almost-prime/Modula-2/almost-prime.mod2 Normal file
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@ -0,0 +1,46 @@
MODULE AlmostPrime;
FROM FormatString IMPORT FormatString;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE KPrime(n,k : INTEGER) : BOOLEAN;
VAR p,f : INTEGER;
BEGIN
f := 0;
p := 2;
WHILE (f<k) AND (p*p<=n) DO
WHILE n MOD p = 0 DO
n := n DIV p;
INC(f)
END;
INC(p)
END;
IF n>1 THEN
RETURN f+1 = k
END;
RETURN f = k
END KPrime;
VAR
buf : ARRAY[0..63] OF CHAR;
i,c,k : INTEGER;
BEGIN
FOR k:=1 TO 5 DO
FormatString("k = %i:", buf, k);
WriteString(buf);
i:=2;
c:=0;
WHILE c<10 DO
IF KPrime(i,k) THEN
FormatString(" %i", buf, i);
WriteString(buf);
INC(c)
END;
INC(i)
END;
WriteLn;
END;
ReadChar;
END AlmostPrime.

28
Task/Almost-prime/Nascom-BASIC/almost-prime.basic Normal file
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@ -0,0 +1,28 @@
10 REM Almost prime
20 FOR K=1 TO 5
30 PRINT "k =";STR$(K);":";
40 I=2
50 C=0
60 IF C>=10 THEN 110
70 AN=I:GOSUB 1000
80 IF ISKPRIME=0 THEN 90
82 REM Print I in 4 fields
84 S$=STR$(I)
86 PRINT SPC(4-LEN(S$));S$;
88 C=C+1
90 I=I+1
100 GOTO 60
110 PRINT
120 NEXT K
130 END
995 REM Check if N (AN) is a K prime
1000 F=0
1010 FOR J=2 TO AN
1020 IF INT(AN/J)*J<>AN THEN 1070
1030 IF F=K THEN ISKPRIME=0:RETURN
1040 F=F+1
1050 AN=INT(AN/J)
1060 GOTO 1020
1070 NEXT J
1080 ISKPRIME=(F=K)
1090 RETURN

23
Task/Almost-prime/Nim/almost-prime.nim Normal file
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@ -0,0 +1,23 @@
proc prime(k: int, listLen: int): seq[int] =
result = @[]
var
test: int = 2
curseur: int = 0
while curseur < listLen:
var
i: int = 2
compte = 0
n = test
while i <= n:
if (n mod i)==0:
n = n div i
compte += 1
else:
i += 1
if compte == k:
result.add(test)
curseur += 1
test += 1
for k in 1..5:
echo "k = ",k," : ",prime(k,10)

27
Task/Almost-prime/Objeck/almost-prime.objeck Normal file
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@ -0,0 +1,27 @@
class Kth_Prime {
function : native : kPrime(n : Int, k : Int) ~ Bool {
f := 0;
for (p := 2; f < k & p*p <= n; p+=1;) {
while (0 = n % p) {
n /= p; f+=1;
};
};
return f + ((n > 1) ? 1 : 0) = k;
}
function : Main(args : String[]) ~ Nil {
for (k := 1; k <= 5; k+=1;) {
"k = {$k}:"->Print();
c := 0;
for (i := 2; c < 10; i+=1;) {
if (kPrime(i, k)) {
" {$i}"->Print();
c+=1;
};
};
'\n'->Print();
};
}
}

14
Task/Almost-prime/Oforth/almost-prime.fth Normal file
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@ -0,0 +1,14 @@
: kprime?( n k -- b )
| i |
0 2 n for: i [
while( n i /mod swap 0 = ) [ ->n 1+ ] drop
]
k ==
;
: table( k -- [] )
| l |
Array new dup ->l
2 while (l size 10 <>) [ dup k kprime? if dup l add then 1+ ]
drop
;

2
Task/Almost-prime/PARI-GP/almost-prime.parigp Normal file
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@ -0,0 +1,2 @@
almost(k)=my(n); for(i=1,10,while(bigomega(n++)!=k,); print1(n", "));
for(k=1,5,almost(k);print)

31
Task/Almost-prime/PHP/almost-prime.php Normal file
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@ -0,0 +1,31 @@
<?php
// Almost prime
function isKPrime($n, $k)
{
$f = 0;
for ($j = 2; $j <= $n; $j++) {
while ($n % $j == 0) {
if ($f == $k)
return false;
$f++;
$n = floor($n / $j);
} // while
} // for $j
return ($f == $k);
}
for ($k = 1; $k <= 5; $k++) {
echo "k = ", $k, ":";
$i = 2;
$c = 0;
while ($c < 10) {
if (isKPrime($i, $k)) {
echo " ", str_pad($i, 3, ' ', STR_PAD_LEFT);
$c++;
}
$i++;
}
echo PHP_EOL;
}
?>

26
Task/Almost-prime/PL-I/almost-prime.pli Normal file
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almost_prime: procedure options(main);
kprime: procedure(nn, k) returns(bit);
declare (n, nn, k, p, f) fixed;
f = 0;
n = nn;
do p=2 repeat(p+1) while(f<k & p*p <= n);
do n=n repeat(n/p) while(mod(n,p) = 0);
f = f+1;
end;
end;
return(f + (n>1) = k);
end kprime;
declare (i, c, k) fixed;
do k=1 to 5;
put edit('k = ',k,':') (A,F(1),A);
c = 0;
do i=2 repeat(i+1) while(c<10);
if kprime(i,k) then do;
put edit(i) (F(4));
c = c+1;
end;
end;
put skip;
end;
end almost_prime;

52
Task/Almost-prime/PL-M/almost-prime.plm Normal file
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@ -0,0 +1,52 @@
100H:
BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS;
EXIT: PROCEDURE; CALL BDOS(0,0); END EXIT;
PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9,S); END PRINT;
PRINT$NUMBER: PROCEDURE (N);
DECLARE S (4) BYTE INITIAL ('...$');
DECLARE P ADDRESS, (N, C BASED P) BYTE;
P = .S(3);
DIGIT:
P = P - 1;
C = N MOD 10 + '0';
N = N / 10;
IF N > 0 THEN GO TO DIGIT;
CALL PRINT(P);
END PRINT$NUMBER;
KPRIME: PROCEDURE (N, K) BYTE;
DECLARE (N, K, P, F) BYTE;
F = 0;
P = 2;
DO WHILE F < K AND P*P <= N;
DO WHILE N MOD P = 0;
N = N/P;
F = F+1;
END;
P = P+1;
END;
IF N > 1 THEN F = F + 1;
RETURN F = K;
END KPRIME;
DECLARE (I, C, K) BYTE;
DO K=1 TO 5;
CALL PRINT(.'K = $');
CALL PRINT$NUMBER(K);
CALL PRINT(.':$');
C = 0;
I = 2;
DO WHILE C < 10;
IF KPRIME(I, K) THEN DO;
CALL PRINT(.' $');
CALL PRINT$NUMBER(I);
C = C+1;
END;
I = I+1;
END;
CALL PRINT(.(13,10,'$'));
END;
CALL EXIT;
EOF

26
Task/Almost-prime/Pascal/almost-prime.pas Normal file
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program AlmostPrime;
{$IFDEF FPC}
{$Mode Delphi}
{$ENDIF}
uses
primtrial;
var
i,K,cnt : longWord;
BEGIN
K := 1;
repeat
cnt := 0;
i := 2;
write('K=',K:2,':');
repeat
if isAlmostPrime(i,K) then
Begin
write(i:6,' ');
inc(cnt);
end;
inc(i);
until cnt = 9;
writeln;
inc(k);
until k > 10;
END.

7
Task/Almost-prime/Perl/almost-prime-1.pl Normal file
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@ -0,0 +1,7 @@
use ntheory qw/factor/;
sub almost {
my($k,$n) = @_;
my $i = 1;
map { $i++ while scalar factor($i) != $k; $i++ } 1..$n;
}
say "$_ : ", join(" ", almost($_,10)) for 1..5;

64
Task/Almost-prime/Perl/almost-prime-2.pl Normal file
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@ -0,0 +1,64 @@
use strict;
use warnings;
sub k_almost_prime;
for my $k ( 1 .. 5 ) {
my $almost = 0;
print join(", ", map {
1 until k_almost_prime ++$almost, $k;
"$almost";
} 1 .. 10), "\n";
}
sub nth_prime;
sub k_almost_prime {
my ($n, $k) = @_;
return if $n <= 1 or $k < 1;
my $which_prime = 0;
for my $count ( 1 .. $k ) {
while( $n % nth_prime $which_prime ) {
++$which_prime;
}
$n /= nth_prime $which_prime;
return if $n == 1 and $count != $k;
}
($n == 1) ? 1 : ();
}
BEGIN {
# This is loosely based on one of the python solutions
# to the RC Sieve of Eratosthenes task.
my @primes = (2, 3, 5, 7);
my $p_iter = 1;
my $p = $primes[$p_iter];
my $q = $p*$p;
my %sieve;
my $candidate = $primes[-1] + 2;
sub nth_prime {
my $n = shift;
return if $n < 0;
OUTER: while( $#primes < $n ) {
while( my $s = delete $sieve{$candidate} ) {
my $next = $s + $candidate;
$next += $s while exists $sieve{$next};
$sieve{$next} = $s;
$candidate += 2;
}
while( $candidate < $q ) {
push @primes, $candidate;
$candidate += 2;
next OUTER if exists $sieve{$candidate};
}
my $twop = 2 * $p;
my $next = $q + $twop;
$next += $twop while exists $sieve{$next};
$sieve{$next} = $twop;
$p = $primes[++$p_iter];
$q = $p * $p;
$candidate += 2;
}
return $primes[$n];
}
}

16
Task/Almost-prime/Phix/almost-prime.phix Normal file
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(phixonline)-->
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">({</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)})</span> <span style="color: #000080;font-style:italic;">-- ie {{1},{2},{3},{4},{5}}</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">found</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">found</span><span style="color: #0000FF;"><</span><span style="color: #000000;">50</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">prime_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">l</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">5</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">])<=</span><span style="color: #000000;">10</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">n</span>
<span style="color: #000000;">found</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"k = %d: "</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%4d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">))&</span><span style="color: #008000;">"\n"</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--

27
Task/Almost-prime/Phixmonti/almost-prime.phixmonti Normal file
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/# Rosetta Code problem: http://rosettacode.org/wiki/Almost_prime
by Galileo, 06/2022 #/
include ..\Utilitys.pmt
def test tps over mod not enddef
def kprime?
>ps >ps
0 ( 2 tps ) for
test while
tps over / int ps> drop >ps
swap 1 + swap
test endwhile
drop
endfor
ps> drop
ps> ==
enddef
5 for >ps
2 ( )
len 10 < while over tps kprime? if over 0 put endif swap 1 + swap len 10 < endwhile
nip ps> drop
endfor
pstack

20
Task/Almost-prime/Picat/almost-prime.picat Normal file
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go =>
N = 10,
Ps = primes(100).take(N),
println(1=Ps),
T = Ps,
foreach(K in 2..5)
T := mul_take(Ps,T,N),
println(K=T)
end,
nl,
foreach(K in 6..25)
T := mul_take(Ps,T,N),
println(K=T)
end,
nl.
% take first N values of L1 x L2
mul_take(L1,L2,N) = [I*J : I in L1, J in L2, I<=J].sort_remove_dups().take(N).
take(L,N) = [L[I] : I in 1..N].

27
Task/Almost-prime/PicoLisp/almost-prime.l Normal file
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(de factor (N)
(make
(let
(D 2
L (1 2 2 . (4 2 4 2 4 6 2 6 .))
M (sqrt N) )
(while (>= M D)
(if (=0 (% N D))
(setq M
(sqrt (setq N (/ N (link D)))) )
(inc 'D (pop 'L)) ) )
(link N) ) ) )
(de almost (N)
(let (X 2 Y 0)
(make
(loop
(when (and (nth (factor X) N) (not (cdr @)))
(link X)
(inc 'Y) )
(T (= 10 Y) 'done)
(inc 'X) ) ) ) )
(for I 5
(println I '-> (almost I) ) )
(bye)

20
Task/Almost-prime/Potion/almost-prime.potion Normal file
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# Converted from C
kprime = (n, k):
p = 2, f = 0
while (f < k && p*p <= n):
while (0 == n % p):
n /= p
f++.
p++.
n = if (n > 1): 1.
else: 0.
f + n == k.
1 to 5 (k):
"k = " print, k print, ":" print
i = 2, c = 0
while (c < 10):
if (kprime(i, k)): " " print, i print, c++.
i++
.
"" say.

37
Task/Almost-prime/Processing/almost-prime.processing Normal file
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void setup() {
for (int i = 1; i <= 5; i++) {
int count = 0;
print("k = " + i + ": ");
int n = 2;
while (count < 10) {
if (isAlmostPrime(i, n)) {
count++;
print(n + " ");
}
n++;
}
println();
}
}
boolean isAlmostPrime(int k, int n) {
if (countPrimeFactors(n) == k) {
return true;
} else {
return false;
}
}
int countPrimeFactors(int n) {
int count = 0;
int i = 2;
while (n > 1) {
if (n % i == 0) {
n /= i;
count++;
} else {
i++;
}
}
return count;
}

20
Task/Almost-prime/Prolog/almost-prime-1.pro Normal file
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% almostPrime(K, +Take, List) succeeds if List can be unified with the
% first Take K-almost-primes.
% Notice that K need not be specified.
% To avoid having to cache or recompute the first Take primes, we define
% almostPrime/3 in terms of almostPrime/4 as follows:
%
almostPrime(K, Take, List) :-
% Compute the list of the first Take primes:
nPrimes(Take, Primes),
almostPrime(K, Take, Primes, List).
almostPrime(1, Take, Primes, Primes).
almostPrime(K, Take, Primes, List) :-
generate(2, K), % generate K >= 2
K1 is K - 1,
almostPrime(K1, Take, Primes, L),
multiplylist( Primes, L, Long),
sort(Long, Sorted), % uniquifies
take(Take, Sorted, List).

40
Task/Almost-prime/Prolog/almost-prime-2.pro Normal file
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nPrimes( M, Primes) :- nPrimes( [2], M, Primes).
nPrimes( Accumulator, I, Primes) :-
next_prime(Accumulator, Prime),
append(Accumulator, [Prime], Next),
length(Next, N),
( N = I -> Primes = Next; nPrimes( Next, I, Primes)).
% next_prime(+Primes, NextPrime) succeeds if NextPrime is the next
% prime after a list, Primes, of consecutive primes starting at 2.
next_prime([2], 3).
next_prime([2|Primes], P) :-
last(Primes, PP),
P2 is PP + 2,
generate(P2, N),
1 is N mod 2, % odd
Max is floor(sqrt(N+1)), % round-off paranoia
forall( (member(Prime, [2|Primes]),
(Prime =< Max -> true
; (!, fail))), N mod Prime > 0 ),
!,
P = N.
% multiply( +A, +List, Answer )
multiply( A, [], [] ).
multiply( A, [X|Xs], [AX|As] ) :-
AX is A * X,
multiply(A, Xs, As).
% multiplylist( L1, L2, List ) succeeds if List is the concatenation of X * L2
% for successive elements X of L1.
multiplylist( [], B, [] ).
multiplylist( [A|As], B, List ) :-
multiply(A, B, L1),
multiplylist(As, B, L2),
append(L1, L2, List).
take(N, List, Head) :-
length(Head, N),
append(Head,X,List).

28
Task/Almost-prime/Prolog/almost-prime-3.pro Normal file
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%%%%% compatibility section %%%%%
:- if(current_prolog_flag(dialect, yap)).
generate(Min, I) :- between(Min, inf, I).
append([],L,L).
append([X|Xs], L, [X|Ls]) :- append(Xs,L,Ls).
:- endif.
:- if(current_prolog_flag(dialect, swi)).
generate(Min, I) :- between(Min, inf, I).
:- endif.
:- if(current_prolog_flag(dialect, yap)).
append([],L,L).
append([X|Xs], L, [X|Ls]) :- append(Xs,L,Ls).
last([X], X).
last([_|Xs],X) :- last(Xs,X).
:- endif.
:- if(current_prolog_flag(dialect, gprolog)).
generate(Min, I) :-
current_prolog_flag(max_integer, Max),
between(Min, Max, I).
:- endif.

43
Task/Almost-prime/PureBasic/almost-prime.basic Normal file
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EnableExplicit
Procedure.b kprime(n.i, k.i)
Define p.i = 2,
f.i = 0
While f < k And p*p <= n
While n % p = 0
n / p
f + 1
Wend
p + 1
Wend
ProcedureReturn Bool(f + Bool(n > 1) = k)
EndProcedure
;___main____
If Not OpenConsole("Almost prime")
End -1
EndIf
Define i.i,
c.i,
k.i
For k = 1 To 5
Print("k = " + Str(k) + ":")
i = 2
c = 0
While c < 10
If kprime(i, k)
Print(RSet(Str(i),4))
c + 1
EndIf
i + 1
Wend
PrintN("")
Next
Input()

19
Task/Almost-prime/Python/almost-prime-1.py Normal file
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from prime_decomposition import decompose
from itertools import islice, count
try:
from functools import reduce
except:
pass
def almostprime(n, k=2):
d = decompose(n)
try:
terms = [next(d) for i in range(k)]
return reduce(int.__mul__, terms, 1) == n
except:
return False
if __name__ == '__main__':
for k in range(1,6):
print('%i: %r' % (k, list(islice((n for n in count() if almostprime(n, k)), 10))))

38
Task/Almost-prime/Python/almost-prime-2.py Normal file
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# k-Almost-primes
# Python 3.6.3
# no imports
# author: manuelcaeiro | https://github.com/manuelcaeiro
def prime_factors(m=2):
for i in range(2, m):
r, q = divmod(m, i)
if not q:
return [i] + prime_factors(r)
return [m]
def k_almost_primes(n, k=2):
multiples = set()
lists = list()
for x in range(k+1):
lists.append([])
for i in range(2, n+1):
if i not in multiples:
if len(lists[1]) < 10:
lists[1].append(i)
multiples.update(range(i*i, n+1, i))
print("k=1: {}".format(lists[1]))
for j in range(2, k+1):
for m in multiples:
l = prime_factors(m)
ll = len(l)
if ll == j and len(lists[j]) < 10:
lists[j].append(m)
print("k={}: {}".format(j, lists[j]))
k_almost_primes(200, 5)
# try:
#k_almost_primes(6000, 10)

19
Task/Almost-prime/Quackery/almost-prime.quackery Normal file
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[ stack ] is quantity ( --> s )
[ stack ] is factors ( --> s )
[ factors put
quantity put
[] 1
[ over size
quantity share != while
1+ dup primefactors
size factors share = if
[ tuck join swap ]
again ]
drop
factors release
quantity release ] is almostprimes ( n n --> [ )
5 times
[ 10 i^ 1+ dup echo sp
almostprimes echo cr ]

49
Task/Almost-prime/R/almost-prime.r Normal file
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#===============================================================
# Find k-Almost-primes
# R implementation
#===============================================================
#---------------------------------------------------------------
# Function for prime factorization from Rosetta Code
#---------------------------------------------------------------
findfactors <- function(n) {
d <- c()
div <- 2; nxt <- 3; rest <- n
while( rest != 1 ) {
while( rest%%div == 0 ) {
d <- c(d, div)
rest <- floor(rest / div)
}
div <- nxt
nxt <- nxt + 2
}
d
}
#---------------------------------------------------------------
# Find k-Almost-primes
#---------------------------------------------------------------
almost_primes <- function(n = 10, k = 5) {
# Set up matrix for storing of the results
res <- matrix(NA, nrow = k, ncol = n)
rownames(res) <- paste("k = ", 1:k, sep = "")
colnames(res) <- rep("", n)
# Loop over k
for (i in 1:k) {
tmp <- 1
while (any(is.na(res[i, ]))) { # Keep looping if there are still missing entries in the result-matrix
if (length(findfactors(tmp)) == i) { # Check number of factors
res[i, which.max(is.na(res[i, ]))] <- tmp
}
tmp <- tmp + 1
}
}
print(res)
}

35
Task/Almost-prime/REXX/almost-prime-1.rexx Normal file
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/*REXX program computes and displays the first N K─almost primes from 1 ──► K. */
parse arg N K . /*get optional arguments from the C.L. */
if N=='' | N=="," then N=10 /*N not specified? Then use default.*/
if K=='' | K=="," then K= 5 /*K " " " " " */
/*W: is the width of K, used for output*/
do m=1 for K; $=2**m; fir=$ /*generate & assign 1st K─almost prime.*/
#=1; if #==N then leave /*#: K─almost primes; Enough are found?*/
#=2; $=$ 3*(2**(m-1)) /*generate & append 2nd K─almost prime.*/
if #==N then leave /*#: K─almost primes; Enough are found?*/
if m==1 then _=fir + fir /* [↓] gen & append 3rd K─almost prime*/
else do; _=9 * (2**(m-2)); #=3; $=$ _; end
do j=_ + m - 1 until #==N /*process an K─almost prime N times.*/
if factr()\==m then iterate /*not the correct K─almost prime? */
#=# + 1; $=$ j /*bump K─almost counter; append it to $*/
end /*j*/ /* [↑] generate N K─almost primes.*/
say right(m, length(K))"─almost ("N') primes:' $
end /*m*/ /* [↑] display a line for each K─prime*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
factr: z=j; do f=0 while z// 2==0; z=z% 2; end /*divisible by 2.*/
do f=f while z// 3==0; z=z% 3; end /*divisible " 3.*/
do f=f while z// 5==0; z=z% 5; end /*divisible " 5.*/
do f=f while z// 7==0; z=z% 7; end /*divisible " 7.*/
do f=f while z//11==0; z=z%11; end /*divisible " 11.*/
do f=f while z//13==0; z=z%13; end /*divisible " 13.*/
do p=17 by 6 while p<=z /*insure P isn't divisible by three. */
parse var p '' -1 _ /*obtain the right─most decimal digit. */
/* [↓] fast check for divisible by 5. */
if _\==5 then do; do f=f+1 while z//p==0; z=z%p; end; f=f-1; end /*÷ by P? */
if _ ==3 then iterate /*fast check for X divisible by five.*/
x=p+2; do f=f+1 while z//x==0; z=z%x; end; f=f-1 /*÷ by X? */
end /*i*/ /* [↑] find all the factors in Z. */
if f==0 then return 1 /*if prime (f==0), then return unity.*/
return f /*return to invoker the number of divs.*/

66
Task/Almost-prime/REXX/almost-prime-2.rexx Normal file
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/*REXX program computes and displays the first N K─almost primes from 1 ──► K. */
parse arg N K . /*obtain optional arguments from the CL*/
if N=='' | N==',' then N=10 /*N not specified? Then use default.*/
if K=='' | K==',' then K= 5 /*K " " " " " */
nn=N; N=abs(N); w=length(K) /*N positive? Then show K─almost primes*/
limit= (2**K) * N / 2 /*this is the limit for most K-primes. */
if N==1 then limit=limit * 2 /* " " " " " a N of 1.*/
if K==1 then limit=limit * 4 /* " " " " " a K─prime " 2.*/
if K==2 then limit=limit * 2 /* " " " " " " " " 4.*/
if K==3 then limit=limit * 3 % 2 /* " " " " " " " " 8.*/
call genPrimes limit + 1 /*generate primes up to the LIMIT + 1.*/
say 'The highest prime computed: ' @.# " (under the limit of " limit').'
say /* [↓] define where 1st K─prime is odd*/
d.=0; d.2= 2; d.3 = 4; d.4 = 7; d.5 = 13; d.6 = 22; d.7 = 38; d.8=63
d.9=102; d.10=168; d.11=268; d.12=426; d.13=673; d.14=1064
d!=0
do m=1 for K; d!=max(d!,d.m) /*generate & assign 1st K─almost prime.*/
mr=right(m,w); mm=m-1
$=; do #=1 to min(N, d!) /*assign some doubled K─almost primes. */
$=$ d.mm.# * 2
end /*#*/
#=#-1
if m==1 then from=2
else from=1 + word($, words($) )
do j=from until #==N /*process an K─almost prime N times.*/
if factr()\==m then iterate /*not the correct K─almost prime? */
#=#+1; $=$ j /*bump K─almost counter; append it to $*/
end /*j*/ /* [↑] generate N K─almost primes.*/
if nn>0 then say mr"─almost ("N') primes:' $
else say ' the last' mr "K─almost prime: " word($, words($))
/* [↓] assign K─almost primes.*/
do q=1 for #; d.m.q=word($,q) ; end /*q*/
do q=1 for #; if d.m.q\==d.mm.q*2 then leave; end /*q*/
/* [↑] count doubly-duplicates*/
/*──── say copies('─',40) 'for ' m", " q-1 'numbers were doubly─duplicated.' ────*/
/*──── say ────*/
end /*m*/ /* [↑] display a line for each K─prime*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
factr: if #.j\==. then return #.j
z=j; do f=0 while z// 2==0; z=z% 2; end /*÷ by 2*/
do f=f while z// 3==0; z=z% 3; end /*÷ " 3*/
do f=f while z// 5==0; z=z% 5; end /*÷ " 5*/
do f=f while z// 7==0; z=z% 7; end /*÷ " 7*/
do f=f while z//11==0; z=z%11; end /*÷ " 11*/
do f=f while z//13==0; z=z%13; end /*÷ " 13*/
do f=f while z//17==0; z=z%17; end /*÷ " 17*/
do f=f while z//19==0; z=z%19; end /*÷ " 19*/
do i=9 while @.i<=z; d=@.i /*divide by some higher primes. */
do f=f while z//d==0; z=z%d; end /*is Z divisible by the prime D ? */
end /*i*/ /* [↑] find all factors in Z. */
if f==0 then f=1; #.j=f; return f /*Is prime (f≡0)? Then return unity. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
genPrimes: arg x; @.=; @.1=2; @.2=3; #.=.; #=2; s.#=@.#**2
do j=@.# +2 by 2 to x /*only find odd primes from here on. */
do p=2 while s.p<=j /*divide by some known low odd primes. */
if j//@.p==0 then iterate j /*Is J divisible by X? Then ¬ prime.*/
end /*p*/ /* [↓] a prime (J) has been found. */
#=#+1; @.#=j; #.j=1; s.#=j*j /*bump prime count, and also assign ···*/
end /*j*/ /* ··· the # of factors, prime, prime².*/
return /* [↑] not an optimal prime generator.*/

25
Task/Almost-prime/Racket/almost-prime.rkt Normal file
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#lang racket
(require (only-in math/number-theory factorize))
(define ((k-almost-prime? k) n)
(= k (for/sum ((f (factorize n))) (cadr f))))
(define KAP-table-values
(for/list ((k (in-range 1 (add1 5))))
(define kap? (k-almost-prime? k))
(for/list ((j (in-range 10)) (i (sequence-filter kap? (in-naturals 1))))
i)))
(define (format-table t)
(define longest-number-length
(add1 (order-of-magnitude (argmax order-of-magnitude (cons (length t) (apply append t))))))
(define (fmt-val v) (~a v #:width longest-number-length #:align 'right))
(string-join
(for/list ((r t) (k (in-naturals 1)))
(string-append
(format "║ k = ~a║ " (fmt-val k))
(string-join (for/list ((c r)) (fmt-val c)) "| ")
"║"))
"\n"))
(displayln (format-table KAP-table-values))

11
Task/Almost-prime/Raku/almost-prime-1.raku Normal file
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sub is-k-almost-prime($n is copy, $k) returns Bool {
loop (my ($p, $f) = 2, 0; $f < $k && $p*$p <= $n; $p++) {
$n /= $p, $f++ while $n %% $p;
}
$f + ($n > 1) == $k;
}
for 1 .. 5 -> $k {
say ~.[^10]
given grep { is-k-almost-prime($_, $k) }, 2 .. *
}

23
Task/Almost-prime/Raku/almost-prime-2.raku Normal file
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constant @primes = 2, |(3, 5, 7 ... *).grep: *.is-prime;
multi sub factors(1) { 1 }
multi sub factors(Int $remainder is copy) {
gather for @primes -> $factor {
# if remainder < factor², we're done
if $factor * $factor > $remainder {
take $remainder if $remainder > 1;
last;
}
# How many times can we divide by this prime?
while $remainder %% $factor {
take $factor;
last if ($remainder div= $factor) === 1;
}
}
}
constant @factory = lazy 0..* Z=> flat (0, 0, map { +factors($_) }, 2..*);
sub almost($n) { map *.key, grep *.value == $n, @factory }
put almost($_)[^10] for 1..5;

33
Task/Almost-prime/Ring/almost-prime.ring Normal file
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for ap = 1 to 5
see "k = " + ap + ":"
aList = []
for n = 1 to 200
num = 0
for nr = 1 to n
if n%nr=0 and isPrime(nr)=1
num = num + 1
pr = nr
while true
pr = pr * nr
if n%pr = 0
num = num + 1
else exit ok
end ok
next
if (ap = 1 and isPrime(n) = 1) or (ap > 1 and num = ap)
add(aList, n)
if len(aList)=10 exit ok ok
next
for m = 1 to len(aList)
see " " + aList[m]
next
see nl
next
func isPrime num
if (num <= 1) return 0 ok
if (num % 2 = 0 and num != 2) return 0 ok
for i = 3 to floor(num / 2) -1 step 2
if (num % i = 0) return 0 ok
next
return 1

8
Task/Almost-prime/Ruby/almost-prime-1.rb Normal file
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require 'prime'
def almost_primes(k=2)
return to_enum(:almost_primes, k) unless block_given?
1.step {|n| yield n if n.prime_division.sum( &:last ) == k }
end
(1..5).each{|k| puts almost_primes(k).take(10).join(", ")}

4
Task/Almost-prime/Ruby/almost-prime-2.rb Normal file
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require 'prime'
p ar = pr = Prime.take(10)
4.times{p ar = ar.product(pr).map{|(a,b)| a*b}.uniq.sort.take(10)}

26
Task/Almost-prime/Run-BASIC/almost-prime.basic Normal file
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for k = 1 to 5
print "k = "; k; " :";
i = 2
c = 0
while c < 10
if kPrime(i, k) then
print " "; using("###", i);
c = c +1
end if
i = i +1
wend
print
next k
end
function kPrime(n, k)
f = 0
for i = 2 to n
while n mod i = 0
if f = k then kPrime = 0
f = f +1
n = int(n / i)
wend
next i
kPrime = abs(f = k)
end function

39
Task/Almost-prime/Rust/almost-prime.rust Normal file
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fn is_kprime(n: u32, k: u32) -> bool {
let mut primes = 0;
let mut f = 2;
let mut rem = n;
while primes < k && rem > 1{
while (rem % f) == 0 && rem > 1{
rem /= f;
primes += 1;
}
f += 1;
}
rem == 1 && primes == k
}
struct KPrimeGen {
k: u32,
n: u32,
}
impl Iterator for KPrimeGen {
type Item = u32;
fn next(&mut self) -> Option<u32> {
self.n += 1;
while !is_kprime(self.n, self.k) {
self.n += 1;
}
Some(self.n)
}
}
fn kprime_generator(k: u32) -> KPrimeGen {
KPrimeGen {k: k, n: 1}
}
fn main() {
for k in 1..6 {
println!("{}: {:?}", k, kprime_generator(k).take(10).collect::<Vec<_>>());
}
}

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