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Ingy döt Net 2023-07-01 11:58:00 -04:00
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commit cb5bb5e222
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2
Task/Ruth-Aaron-numbers/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Ruth-Aaron_numbers

32
Task/Ruth-Aaron-numbers/00-TASK.txt Normal file
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A '''Ruth–Aaron''' pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime divisors of each integer are equal. So called because 714 is Babe Ruth's lifetime home run record; Hank Aaron's 715th home run broke this record and 714 and 715 have the same prime divisor sum.
A '''Ruth–Aaron''' triple consists of '''''three''''' consecutive integers with the same properties.
There is a second variant of '''Ruth–Aaron''' numbers, one which uses prime ''factors'' rather than prime ''divisors''. The difference; divisors are unique, factors may be repeated. The 714, 715 pair appears in both, so the name still fits.
It is common to refer to each '''Ruth–Aaron''' group by the first number in it.
;Task
* Find and show, here on this page, the first '''30''' '''Ruth-Aaron numbers''' (factors).
* Find and show, here on this page, the first '''30''' '''Ruth-Aaron numbers''' (divisors).
;Stretch
* Find and show the first '''Ruth-Aaron triple''' (factors).
* Find and show the first '''Ruth-Aaron triple''' (divisors).
;See also
;*[[wp:Ruth–Aaron_pair|Wikipedia: Ruth–Aaron pair]]
;*[[oeis:A006145|OEIS:A006145 - Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1]]
;*[[oeis:A039752|OEIS:A039752 - Ruth-Aaron numbers (2): sum of prime divisors of n = sum of prime divisors of n+1 (both taken with multiplicity)]]

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Task/Ruth-Aaron-numbers/ALGOL-68/ruth-aaron-numbers.alg Normal file
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BEGIN # find Ruth-Aaron pairs - pairs of consecutive integers where the sum #
# of the prime factors or divisors are equal #
INT max number = 99 000 000; # max number we will consider #
# construct a sieve of primes up to max number #
[ 1 : max number ]BOOL prime;
prime[ 1 ] := FALSE;
prime[ 2 ] := TRUE;
FOR i FROM 3 BY 2 TO UPB prime DO prime[ i ] := TRUE OD;
FOR i FROM 4 BY 2 TO UPB prime DO prime[ i ] := FALSE OD;
FOR i FROM 3 BY 2 TO ENTIER sqrt( UPB prime ) DO
IF prime[ i ] THEN
FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD
FI
OD;
# construct the sums of prime divisors up to max number #
[ 1 : max number ]INT ps; FOR n TO max number DO ps[ n ] := 0 OD;
FOR n TO max number DO
IF prime[ n ] THEN
FOR j FROM n BY n TO max number DO ps[ j ] PLUSAB n OD
FI
OD;
INT max count = 30;
# first max count Ruth-Aaron (divisors) numbers #
[ 1 : max count ]INT dra;
INT count := 0;
INT prev sum := 0;
FOR n FROM 2 WHILE count < max count DO
INT this sum = ps[ n ];
IF prev sum = this sum THEN
# found another Ruth-Aaron number #
count PLUSAB 1;
IF count <= max count THEN dra[ count ] := n - 1 FI
FI;
prev sum := this sum
OD;
# first triple #
INT dra3 := 0;
INT pprev sum := ps[ 1 ];
prev sum := ps[ 2 ];
FOR n FROM 3 WHILE dra3 = 0 DO
INT this sum = ps[ n ];
IF prev sum = this sum THEN
IF pprev sum = this sum THEN
# found a Ruth-Aaron triple #
dra3 := n - 2
FI
FI;
pprev sum := prev sum;
prev sum := this sum
OD;
# replace ps with the prime factor count #
INT root max number = ENTIER sqrt( max number );
FOR n FROM 2 TO root max number DO
IF prime[ n ] THEN
INT p := n * n;
WHILE p < root max number DO
FOR j FROM p BY p TO max number DO ps[ j ] PLUSAB n OD;
p TIMESAB n
OD
FI
OD;
# first max count Ruth-Aaron (factors) numbers #
[ 1 : max count ]INT fra;
prev sum := ps[ 1 ];
count := 0;
FOR n FROM 2 WHILE count < 30 DO
INT this sum = ps[ n ];
IF prev sum = this sum THEN
# found another Ruth-Aaron number #
count PLUSAB 1;
fra[ count ] := n - 1
FI;
prev sum := this sum
OD;
# first triple #
prev sum := 0;
count := 0;
INT fra3 := 0;
FOR n FROM 2 WHILE fra3 = 0 DO
INT this sum = ps[ n ];
IF prev sum = this sum AND pprev sum = this sum THEN
# found a Ruth-Aaron triple #
fra3 := n - 2
FI;
pprev sum := prev sum;
prev sum := this sum
OD;
# show the numbers #
print( ( "The first ", whole( max count, 0 ), " Ruth-Aaron numbers (factors):", newline ) );
FOR n TO max count DO
print( ( whole( fra[ n ], - 6 ) ) );
IF n MOD 10 = 0 THEN print( ( newline ) ) FI
OD;
# divisors #
print( ( "The first ", whole( max count, 0 ), " Ruth-Aaron numbers (divisors):", newline ) );
FOR n TO max count DO
print( ( whole( dra[ n ], - 6 ) ) );
IF n MOD 10 = 0 THEN print( ( newline ) ) FI
OD;
# triples #
print( ( newline, "First Ruth-Aaron triple (factors): ", whole( fra3, 0 ) ) );
print( ( newline, "First Ruth-Aaron triple (divisors): ", whole( dra3, 0 ) ) )
END

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Task/Ruth-Aaron-numbers/Arturo/ruth-aaron-numbers.arturo Normal file
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fRuthAaron?: function [n]-> (sum factors.prime n) = sum factors.prime n+1
dRuthAaron?: function [n]-> (sum unique factors.prime n) = sum unique factors.prime n+1
print "First 30 Ruth-Aaron numbers (factors):"
loop split.every: 10 select.first:30 1..∞ => fRuthAaron? 'x ->
print map x 's -> pad to :string s 5
print ""
print "First 30 Ruth-Aaron numbers (divisors):"
loop split.every: 10 select.first:30 1..∞ => dRuthAaron? 'x ->
print map x 's -> pad to :string s 5

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Task/Ruth-Aaron-numbers/C++/ruth-aaron-numbers.cpp Normal file
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#include <iomanip>
#include <iostream>
int prime_factor_sum(int n) {
int sum = 0;
for (; (n & 1) == 0; n >>= 1)
sum += 2;
for (int p = 3, sq = 9; sq <= n; p += 2) {
for (; n % p == 0; n /= p)
sum += p;
sq += (p + 1) << 2;
}
if (n > 1)
sum += n;
return sum;
}
int prime_divisor_sum(int n) {
int sum = 0;
if ((n & 1) == 0) {
sum += 2;
n >>= 1;
while ((n & 1) == 0)
n >>= 1;
}
for (int p = 3, sq = 9; sq <= n; p += 2) {
if (n % p == 0) {
sum += p;
n /= p;
while (n % p == 0)
n /= p;
}
sq += (p + 1) << 2;
}
if (n > 1)
sum += n;
return sum;
}
int main() {
const int limit = 30;
int dsum1 = 0, fsum1 = 0, dsum2 = 0, fsum2 = 0;
std::cout << "First " << limit << " Ruth-Aaron numbers (factors):\n";
for (int n = 2, count = 0; count < limit; ++n) {
fsum2 = prime_factor_sum(n);
if (fsum1 == fsum2) {
++count;
std::cout << std::setw(5) << n - 1
<< (count % 10 == 0 ? '\n' : ' ');
}
fsum1 = fsum2;
}
std::cout << "\nFirst " << limit << " Ruth-Aaron numbers (divisors):\n";
for (int n = 2, count = 0; count < limit; ++n) {
dsum2 = prime_divisor_sum(n);
if (dsum1 == dsum2) {
++count;
std::cout << std::setw(5) << n - 1
<< (count % 10 == 0 ? '\n' : ' ');
}
dsum1 = dsum2;
}
dsum1 = 0, fsum1 = 0, dsum2 = 0, fsum2 = 0;
for (int n = 2;; ++n) {
int fsum3 = prime_factor_sum(n);
if (fsum1 == fsum2 && fsum2 == fsum3) {
std::cout << "\nFirst Ruth-Aaron triple (factors): " << n - 2
<< '\n';
break;
}
fsum1 = fsum2;
fsum2 = fsum3;
}
for (int n = 2;; ++n) {
int dsum3 = prime_divisor_sum(n);
if (dsum1 == dsum2 && dsum2 == dsum3) {
std::cout << "\nFirst Ruth-Aaron triple (divisors): " << n - 2
<< '\n';
break;
}
dsum1 = dsum2;
dsum2 = dsum3;
}
}

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Task/Ruth-Aaron-numbers/Delphi/ruth-aaron-numbers.delphi Normal file
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{These routines would normally be in a library, but are shown here for clarity}
function IsPrime(N: int64): boolean;
{Fast, optimised prime test}
var I,Stop: int64;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N+0.0));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;
procedure StoreNumber(N: integer; var IA: TIntegerDynArray);
{Expand and store number in array}
begin
SetLength(IA,Length(IA)+1);
IA[High(IA)]:=N;
end;
procedure GetPrimeFactors(N: integer; var Facts: TIntegerDynArray);
{Get all the prime factors of a number}
var I: integer;
begin
I:=2;
SetLength(Facts,0);
repeat
begin
if (N mod I) = 0 then
begin
StoreNumber(I,Facts);
N:=N div I;
end
else I:=GetNextPrime(I);
end
until N=1;
end;
procedure GetPrimeDivisors(N: integer; var Facts: TIntegerDynArray);
{Get all unique prime factors of a number}
var I: integer;
begin
I:=2;
SetLength(Facts,0);
repeat
begin
if (N mod I) = 0 then
begin
StoreNumber(I,Facts);
N:=N div I;
while (N mod I) = 0 do N:=N div I;
end
else I:=GetNextPrime(I);
end
until N=1;
end;
{------------------------------------------------------------}
procedure RuthAaronNumbers(Memo: TMemo; UseFactors: boolean);
var N,Sum1,Sum2,Cnt: integer;
var S: string;
function GetFactorSum(N: integer): integer;
{Get the sum of the prime factors or divisors}
var IA: TIntegerDynArray;
var I: integer;
begin
if UseFactors then GetPrimeFactors(N,IA)
else GetPrimeDivisors(N,IA);
Result:=0;
for I:=0 to High(IA) do Result:=Result+IA[I];
end;
begin
Cnt:=0;
S:='';
{Get first sum}
Sum1:=GetFactorSum(1);
for N:=1 to High(integer) do
begin
{Get next sum}
Sum2:=GetFactorSum(N+1);
{Look for matching sums = Ruth-Aaron numbers}
if Sum1=Sum2 then
begin
Inc(Cnt);
S:=S+Format('%6D',[N]);
if Cnt>=30 then break;
If (Cnt mod 10)=0 then S:=S+CRLF;
end;
Sum1:=Sum2;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('Count = '+IntToStr(Cnt));
end;
procedure ShowRuthAaronNumbers(Memo: TMemo);
begin
Memo.Lines.Add('The first 30 Ruth-Aaron numbers using factors');
RuthAaronNumbers(Memo, True);
Memo.Lines.Add('The first 30 Ruth-Aaron numbers using divisors');
RuthAaronNumbers(Memo, False);
end;

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Task/Ruth-Aaron-numbers/Factor/ruth-aaron-numbers.factor Normal file
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USING: assocs.extras grouping io kernel lists lists.lazy math
math.primes.factors prettyprint ranges sequences ;
: pair-same? ( ... n quot: ( ... m -- ... n ) -- ... ? )
[ dup 1 + ] dip same? ; inline
: RA-f? ( n -- ? ) [ factors sum ] pair-same? ;
: RA-d? ( n -- ? ) [ group-factors sum-keys ] pair-same? ;
: filter-naturals ( quot -- list ) 1 lfrom swap lfilter ; inline
: RA-f ( -- list ) [ RA-f? ] filter-naturals ;
: RA-d ( -- list ) [ RA-d? ] filter-naturals ;
: list. ( list -- )
30 swap ltake list>array 10 group simple-table. ;
"First 30 Ruth-Aaron numbers (factors):" print
RA-f list. nl
"First 30 Ruth-Aaron numbers (divisors):" print
RA-d list.

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Task/Ruth-Aaron-numbers/Free-Pascal/ruth-aaron-numbers.pas Normal file
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program RuthAaronNumb;
// gets factors of consecutive integers fast
// limited to 1.2e11
{$IFDEF FPC}
{$MODE DELPHI} {$OPTIMIZATION ON,ALL} {$COPERATORS ON}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF}
uses
sysutils,
strutils //Numb2USA
{$IFDEF WINDOWS},Windows{$ENDIF}
;
//######################################################################
//prime decomposition
const
//HCN(86) > 1.2E11 = 128,501,493,120 count of divs = 4096 7 3 1 1 1 1 1 1 1
HCN_DivCnt = 4096;
//used odd size for test only
SizePrDeFe = 32768;//*72 <= 64kb level I or 2 Mb ~ level 2 cache
type
tItem = Uint64;
tDivisors = array [0..HCN_DivCnt] of tItem;
tpDivisor = pUint64;
tdigits = array [0..31] of Uint32;
//the first number with 11 different prime factors =
//2*3*5*7*11*13*17*19*23*29*31 = 2E11
//56 byte
tprimeFac = packed record
pfSumOfDivs,
pfRemain : Uint64;
pfDivCnt : Uint32;
pfMaxIdx : Uint32;
pfpotPrimIdx : array[0..9] of word;
pfpotMax : array[0..11] of byte;
end;
tpPrimeFac = ^tprimeFac;
tPrimeDecompField = array[0..SizePrDeFe-1] of tprimeFac;
tPrimes = array[0..65535] of Uint32;
var
{$ALIGN 8}
SmallPrimes: tPrimes;
{$ALIGN 32}
PrimeDecompField :tPrimeDecompField;
pdfIDX,pdfOfs: NativeInt;
procedure InitSmallPrimes;
//get primes. #0..65535.Sieving only odd numbers
const
MAXLIMIT = (821641-1) shr 1;
var
pr : array[0..MAXLIMIT] of byte;
p,j,d,flipflop :NativeUInt;
Begin
SmallPrimes[0] := 2;
fillchar(pr[0],SizeOf(pr),#0);
p := 0;
repeat
repeat
p +=1
until pr[p]= 0;
j := (p+1)*p*2;
if j>MAXLIMIT then
BREAK;
d := 2*p+1;
repeat
pr[j] := 1;
j += d;
until j>MAXLIMIT;
until false;
SmallPrimes[1] := 3;
SmallPrimes[2] := 5;
j := 3;
d := 7;
flipflop := (2+1)-1;//7+2*2,11+2*1,13,17,19,23
p := 3;
repeat
if pr[p] = 0 then
begin
SmallPrimes[j] := d;
inc(j);
end;
d += 2*flipflop;
p+=flipflop;
flipflop := 3-flipflop;
until (p > MAXLIMIT) OR (j>High(SmallPrimes));
end;
function OutPots(pD:tpPrimeFac;n:NativeInt):Ansistring;
var
s: String[31];
chk,p,i: NativeInt;
Begin
str(n,s);
result := Format('%15s : ',[Numb2USA(s)]);
with pd^ do
begin
chk := 1;
For n := 0 to pfMaxIdx-1 do
Begin
if n>0 then
result += '*';
p := SmallPrimes[pfpotPrimIdx[n]];
chk *= p;
str(p,s);
result += s;
i := pfpotMax[n];
if i >1 then
Begin
str(pfpotMax[n],s);
result += '^'+s;
repeat
chk *= p;
dec(i);
until i <= 1;
end;
end;
p := pfRemain;
If p >1 then
Begin
str(p,s);
chk *= p;
result += '*'+s;
end;
end;
end;
function CnvtoBASE(var dgt:tDigits;n:Uint64;base:NativeUint):NativeInt;
//n must be multiple of base aka n mod base must be 0
var
q,r: Uint64;
i : NativeInt;
Begin
fillchar(dgt,SizeOf(dgt),#0);
i := 0;
n := n div base;
result := 0;
repeat
r := n;
q := n div base;
r -= q*base;
n := q;
dgt[i] := r;
inc(i);
until (q = 0);
//searching lowest pot in base
result := 0;
while (result<i) AND (dgt[result] = 0) do
inc(result);
inc(result);
end;
function IncByBaseInBase(var dgt:tDigits;base:NativeInt):NativeInt;
var
q :NativeInt;
Begin
result := 0;
q := dgt[result]+1;
if q = base then
repeat
dgt[result] := 0;
inc(result);
q := dgt[result]+1;
until q <> base;
dgt[result] := q;
result +=1;
end;
function SieveOneSieve(var pdf:tPrimeDecompField):boolean;
var
dgt:tDigits;
i,j,k,pr,fac,n,MaxP : Uint64;
begin
n := pdfOfs;
if n+SizePrDeFe >= sqr(SmallPrimes[High(SmallPrimes)]) then
EXIT(FALSE);
//init
for i := 0 to SizePrDeFe-1 do
begin
with pdf[i] do
Begin
pfDivCnt := 1;
pfSumOfDivs := 1;
pfRemain := n+i;
pfMaxIdx := 0;
pfpotPrimIdx[0] := 0;
pfpotMax[0] := 0;
end;
end;
//first factor 2. Make n+i even
i := (pdfIdx+n) AND 1;
IF (n = 0) AND (pdfIdx<2) then
i := 2;
repeat
with pdf[i] do
begin
j := BsfQWord(n+i);
pfMaxIdx := 1;
pfpotPrimIdx[0] := 0;
pfpotMax[0] := j;
pfRemain := (n+i) shr j;
pfSumOfDivs := (Uint64(1) shl (j+1))-1;
pfDivCnt := j+1;
end;
i += 2;
until i >=SizePrDeFe;
//i now index in SmallPrimes
i := 0;
maxP := trunc(sqrt(n+SizePrDeFe))+1;
repeat
//search next prime that is in bounds of sieve
if n = 0 then
begin
repeat
inc(i);
pr := SmallPrimes[i];
k := pr-n MOD pr;
if k < SizePrDeFe then
break;
until pr > MaxP;
end
else
begin
repeat
inc(i);
pr := SmallPrimes[i];
k := pr-n MOD pr;
if (k = pr) AND (n>0) then
k:= 0;
if k < SizePrDeFe then
break;
until pr > MaxP;
end;
//no need to use higher primes
if pr*pr > n+SizePrDeFe then
BREAK;
//j is power of prime
j := CnvtoBASE(dgt,n+k,pr);
repeat
with pdf[k] do
Begin
pfpotPrimIdx[pfMaxIdx] := i;
pfpotMax[pfMaxIdx] := j;
pfDivCnt *= j+1;
fac := pr;
repeat
pfRemain := pfRemain DIV pr;
dec(j);
fac *= pr;
until j<= 0;
pfSumOfDivs *= (fac-1)DIV(pr-1);
inc(pfMaxIdx);
k += pr;
j := IncByBaseInBase(dgt,pr);
end;
until k >= SizePrDeFe;
until false;
//correct sum of & count of divisors
for i := 0 to High(pdf) do
Begin
with pdf[i] do
begin
j := pfRemain;
if j <> 1 then
begin
pfSumOFDivs *= (j+1);
pfDivCnt *=2;
end;
end;
end;
result := true;
end;
function NextSieve:boolean;
begin
dec(pdfIDX,SizePrDeFe);
inc(pdfOfs,SizePrDeFe);
result := SieveOneSieve(PrimeDecompField);
end;
function GetNextPrimeDecomp:tpPrimeFac;
begin
if pdfIDX >= SizePrDeFe then
if Not(NextSieve) then
EXIT(NIL);
result := @PrimeDecompField[pdfIDX];
inc(pdfIDX);
end;
function Init_Sieve(n:NativeUint):boolean;
//Init Sieve pdfIdx,pdfOfs are Global
begin
pdfIdx := n MOD SizePrDeFe;
pdfOfs := n-pdfIdx;
result := SieveOneSieve(PrimeDecompField);
end;
//end prime decomposition
//######################################################################
procedure Get_RA_Prime(cntlimit:NativeUInt;useFactors:Boolean);
var
pPrimeDecomp :tpPrimeFac;
pr,sum0,sum1,n,i,cnt : NativeUInt;
begin
write('First 30 Ruth-Aaron numbers (');
if useFactors then
writeln('factors ):')
else
writeln('divisors ):');
cnt := 0;
sum1:= 0;
n := 2;
Init_Sieve(n);
repeat
pPrimeDecomp:= GetNextPrimeDecomp;
with pPrimeDecomp^ do
begin
sum0:= pfRemain;
//if not(prime)
if (sum0 <> n) then
begin
if sum0 = 1 then
sum0 := 0;
For i := 0 to pfMaxIdx-1 do
begin
pr := smallprimes[pfpotPrimIdx[i]];
if useFactors then
sum0 += pr*pfpotMax[i]
else
sum0 += pr;
end;
if sum1 = sum0 then
begin
write(n-1:10);
inc(cnt);
if cnt mod 8 = 0 then
writeln;
end;
sum1 := sum0;
end
else
sum1:= 0;
end;
inc(n);
until cnt>=cntlimit;
writeln;
end;
function findfirstTripplesFactor(useFactors:boolean):NativeUint;
var
pPrimeDecomp :tpPrimeFac;
pr,sum0,sum1,sum2,i : NativeUInt;
begin
sum1:= 0;
sum2:= 0;
result:= 2;
Init_Sieve(result);
repeat
pPrimeDecomp:= GetNextPrimeDecomp;
with pPrimeDecomp^ do
begin
sum0:= pfRemain;
//if not(prime)
if (sum0 <> result) then
begin
if sum0 = 1 then
sum0 := 0;
For i := 0 to pfMaxIdx-1 do
begin
pr := smallprimes[pfpotPrimIdx[i]];
if useFactors then
pr *= pfpotMax[i];
sum0 += pr
end;
if (sum2 = sum0) AND (sum1=sum0) then
Exit(result-2);
end
else
sum0 := 0;
sum2:= sum1;
sum1 := sum0;
end;
inc(result);
until false
end;
var
T1,T0 : Int64;
Begin
T0 := GetTickCount64;
InitSmallPrimes;
Get_RA_Prime(30,false);
Get_RA_Prime(30,true);
writeln('used time: ',GettickCount64-T0,' ms');
writeln;
writeln('First Ruth-Aaron triple (factors) :');
T0 := GetTickCount64;
writeln(findfirstTripplesFactor(true):10,' in ',GettickCount64-T0,' ms');
writeln;
writeln('First Ruth-Aaron triple (divisors):');
T0 := GetTickCount64;
writeln(findfirstTripplesFactor(false):10,' in ',GettickCount64-T0,' ms');
end.

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Task/Ruth-Aaron-numbers/FreeBASIC/ruth-aaron-numbers.basic Normal file
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Function DivSum(N As Integer, AllDiv As Boolean) As Integer
Dim As Integer Q, F = 2, F0 = 0, S1 = 0
Do
Q = N/F
If (N Mod F) = 0 Then
If AllDiv Then
S1 += F
Else
If F <> F0 Then S1 += F : F0 = F
End If
N = Q
Else
F += 1
End If
Loop Until F > N
Return S1
End Function
Sub Ruth_Aaron(AllDiv As Boolean)
Dim As Integer S, C = 0, S0 = 0, N = 2
Do
S = DivSum(N, AllDiv)
If S = S0 Then
Print Using "######"; N-1;
C += 1
If (C Mod 10) = 0 Then Print
End If
S0 = S
N += 1
Loop Until C >= 30
End Sub
Print "First 30 Ruth-Aaron numbers (factors):"
Ruth_Aaron(True) ' https://oeis.org/A039752
Print !"\nFirst 30 Ruth-Aaron numbers (divisors):"
Ruth_Aaron(False) ' https://oeis.org/A006145
Sleep

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Task/Ruth-Aaron-numbers/Go/ruth-aaron-numbers.go Normal file
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package main
import (
"fmt"
"rcu"
)
func prune(a []int) []int {
prev := a[0]
b := []int{prev}
for i := 1; i < len(a); i++ {
if a[i] != prev {
b = append(b, a[i])
prev = a[i]
}
}
return b
}
func main() {
var resF, resD, resT, factors1 []int
factors2 := []int{2}
factors3 := []int{3}
var sum1, sum2, sum3 int = 0, 2, 3
var countF, countD, countT int
for n := 2; countT < 1 || countD < 30 || countF < 30; n++ {
factors1 = factors2
factors2 = factors3
factors3 = rcu.PrimeFactors(n + 2)
sum1 = sum2
sum2 = sum3
sum3 = rcu.SumInts(factors3)
if countF < 30 && sum1 == sum2 {
resF = append(resF, n)
countF++
}
if sum1 == sum2 && sum2 == sum3 {
resT = append(resT, n)
countT++
}
if countD < 30 {
factors4 := make([]int, len(factors1))
copy(factors4, factors1)
factors5 := make([]int, len(factors2))
copy(factors5, factors2)
factors4 = prune(factors4)
factors5 = prune(factors5)
if rcu.SumInts(factors4) == rcu.SumInts(factors5) {
resD = append(resD, n)
countD++
}
}
}
fmt.Println("First 30 Ruth-Aaron numbers (factors):")
fmt.Println(resF)
fmt.Println("\nFirst 30 Ruth-Aaron numbers (divisors):")
fmt.Println(resD)
fmt.Println("\nFirst Ruth-Aaron triple (factors):")
fmt.Println(resT[0])
resT = resT[:0]
factors1 = factors1[:0]
factors2 = factors2[:1]
factors2[0] = 2
factors3 = factors3[:1]
factors3[0] = 3
countT = 0
for n := 2; countT < 1; n++ {
factors1 = factors2
factors2 = factors3
factors3 = prune(rcu.PrimeFactors(n + 2))
sum1 = sum2
sum2 = sum3
sum3 = rcu.SumInts(factors3)
if sum1 == sum2 && sum2 == sum3 {
resT = append(resT, n)
countT++
}
}
fmt.Println("\nFirst Ruth-Aaron triple (divisors):")
fmt.Println(resT[0])
}

51
Task/Ruth-Aaron-numbers/Haskell/ruth-aaron-numbers.hs Normal file
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import qualified Data.Set as S
import Data.List.Split ( chunksOf )
divisors :: Int -> [Int]
divisors n = [d | d <- [2 .. n] , mod n d == 0]
--for obvious theoretical reasons the smallest divisor of a number bare 1
--must be prime
primeFactors :: Int -> [Int]
primeFactors n = snd $ until ( (== 1) . fst ) step (n , [] )
where
step :: (Int , [Int] ) -> (Int , [Int] )
step (n , li) = ( div n h , li ++ [h] )
where
h :: Int
h = head $ divisors n
primeDivisors :: Int -> [Int]
primeDivisors n = S.toList $ S.fromList $ primeFactors n
solution :: (Int -> [Int] ) -> [Int]
solution f = snd $ until ( (== 30 ) . length . snd ) step ([2 , 3] , [] )
where
step :: ([Int] , [Int] ) -> ([Int] , [Int])
step ( neighbours , ranums ) = ( map ( + 1 ) neighbours , if (sum $ f
$ head neighbours ) == (sum $ f $ last neighbours) then
ranums ++ [ head neighbours ] else ranums )
formatNumber :: Int -> String -> String
formatNumber width num
|width > l = replicate ( width -l ) ' ' ++ num
|width == l = num
|width < l = num
where
l = length num
main :: IO ( )
main = do
let ruth_aaron_pairs = solution primeFactors
maxlen = length $ show $ last ruth_aaron_pairs
numberlines = chunksOf 8 $ map show ruth_aaron_pairs
ruth_aaron_divisors = solution primeDivisors
maxlen2 = length $ show $ last ruth_aaron_divisors
numberlines2 = chunksOf 8 $ map show ruth_aaron_divisors
putStrLn "First 30 Ruth-Aaaron numbers ( factors ) :"
mapM_ (\nlin -> putStrLn $ foldl1 ( ++ ) $ map (\st -> formatNumber (maxlen + 2) st )
nlin ) numberlines
putStrLn " "
putStrLn "First 30 Ruth-Aaron numbers( divisors ):"
mapM_ (\nlin -> putStrLn $ foldl1 ( ++ ) $ map (\st -> formatNumber (maxlen2 + 2) st )
nlin ) numberlines2

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NB. using factors
30{.1 2+/~I. 2 =/\ +/@q: 1+i.100000
5 6
8 9
15 16
77 78
125 126
714 715
948 949
1330 1331
1520 1521
1862 1863
2491 2492
3248 3249
4185 4186
4191 4192
5405 5406
5560 5561
5959 5960
6867 6868
8280 8281
8463 8464
10647 10648
12351 12352
14587 14588
16932 16933
17080 17081
18490 18491
20450 20451
24895 24896
26642 26643
26649 26650
NB. using divisors
30{.1 2+/~I. 2 =/\ (+/@{.@q:~&__) 1+i.100000
5 6
24 25
49 50
77 78
104 105
153 154
369 370
492 493
714 715
1682 1683
2107 2108
2299 2300
2600 2601
2783 2784
5405 5406
6556 6557
6811 6812
8855 8856
9800 9801
12726 12727
13775 13776
18655 18656
21183 21184
24024 24025
24432 24433
24880 24881
25839 25840
26642 26643
35456 35457
40081 40082

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import java.util.ArrayList;
import java.util.BitSet;
import java.util.Collection;
import java.util.HashSet;
import java.util.List;
public final class RuthAaronNumbers {
public static void main(String[] aArgs) {
System.out.println("The first 30 Ruth-Aaron numbers (factors):");
firstRuthAaronNumbers(30, NumberType.FACTOR);
System.out.println("The first 30 Ruth-Aaron numbers (divisors):");
firstRuthAaronNumbers(30, NumberType.DIVISOR);
System.out.println("First Ruth-Aaron triple (factors): " + firstRuthAaronTriple(NumberType.FACTOR));
System.out.println();
System.out.println("First Ruth-Aaron triple (divisors): " + firstRuthAaronTriple(NumberType.DIVISOR));
System.out.println();
}
private enum NumberType { DIVISOR, FACTOR }
private static void firstRuthAaronNumbers(int aCount, NumberType aNumberType) {
primeSumOne = 0;
primeSumTwo = 0;
for ( int n = 2, count = 0; count < aCount; n++ ) {
primeSumTwo = switch ( aNumberType ) {
case DIVISOR -> primeDivisorSum(n);
case FACTOR -> primeFactorSum(n);
};
if ( primeSumOne == primeSumTwo ) {
count += 1;
System.out.print(String.format("%6d", n - 1));
if ( count == aCount / 2 ) {
System.out.println();
}
}
primeSumOne = primeSumTwo;
}
System.out.println();
System.out.println();
}
private static int firstRuthAaronTriple(NumberType aNumberType) {
primeSumOne = 0;
primeSumTwo = 0;
primeSumThree = 0;
int n = 2;
boolean found = false;
while ( ! found ) {
primeSumThree = switch ( aNumberType ) {
case DIVISOR -> primeDivisorSum(n);
case FACTOR -> primeFactorSum(n);
};
if ( primeSumOne == primeSumTwo && primeSumTwo == primeSumThree ) {
found = true;
}
n += 1;
primeSumOne = primeSumTwo;
primeSumTwo = primeSumThree;
}
return n - 2;
}
private static int primeDivisorSum(int aNumber) {
return primeSum(aNumber, new HashSet<Integer>());
}
private static int primeFactorSum(int aNumber) {
return primeSum(aNumber, new ArrayList<Integer>());
}
private static int primeSum(int aNumber, Collection<Integer> aCollection) {
Collection<Integer> values = aCollection;
for ( int i = 0, prime = 2; prime * prime <= aNumber; i++ ) {
while ( aNumber % prime == 0 ) {
aNumber /= prime;
values.add(prime);
}
prime = primes.get(i + 1);
}
if ( aNumber > 1 ) {
values.add(aNumber);
}
return values.stream().reduce(0, ( l, r ) -> l + r );
}
private static List<Integer> listPrimeNumbersUpTo(int aNumber) {
BitSet sieve = new BitSet(aNumber + 1);
sieve.set(2, aNumber + 1);
final int squareRoot = (int) Math.sqrt(aNumber);
for ( int i = 2; i <= squareRoot; i = sieve.nextSetBit(i + 1) ) {
for ( int j = i * i; j <= aNumber; j += i ) {
sieve.clear(j);
}
}
List<Integer> result = new ArrayList<Integer>(sieve.cardinality());
for ( int i = 2; i >= 0; i = sieve.nextSetBit(i + 1) ) {
result.add(i);
}
return result;
}
private static int primeSumOne, primeSumTwo, primeSumThree;
private static List<Integer> primes = listPrimeNumbersUpTo(50_000);
}

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Task/Ruth-Aaron-numbers/Julia/ruth-aaron-numbers.julia Normal file
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using Lazy
using Primes
sumprimedivisors(n) = sum([p[1] for p in factor(n)])
ruthaaron(n) = sumprimedivisors(n) == sumprimedivisors(n + 1)
ruthaarontriple(n) = sumprimedivisors(n) == sumprimedivisors(n + 1) ==
sumprimedivisors(n + 2)
sumprimefactors(n) = sum([p[1] * p[2] for p in factor(n)])
ruthaaronfactors(n) = sumprimefactors(n) == sumprimefactors(n + 1)
ruthaaronfactorstriple(n) = sumprimefactors(n) == sumprimefactors(n + 1) ==
sumprimefactors(n + 2)
raseq = @>> Lazy.range() filter(ruthaaron)
rafseq = @>> Lazy.range() filter(ruthaaronfactors)
println("30 Ruth Aaron numbers:")
foreach(p -> print(lpad(p[2], 6), p[1] % 10 == 0 ? "\n" : ""),
enumerate(collect(take(30, raseq))))
println("\n30 Ruth Aaron factor numbers:")
foreach(p -> print(lpad(p[2], 6), p[1] % 10 == 0 ? "\n" : ""),
enumerate(collect(take(30, rafseq))))
println("\nRuth Aaron triple starts at: ", findfirst(ruthaarontriple, 1:100000000))
println("\nRuth Aaron factor triple starts at: ", findfirst(ruthaaronfactorstriple, 1:10000000))

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Task/Ruth-Aaron-numbers/Nim/ruth-aaron-numbers.nim Normal file
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import std/strformat
template isEven(n: Natural): bool = (n and 1) == 0
func primeFactorSum(n: int): int =
var n = n
while n.isEven:
inc result, 2
n = n shr 1
var p = 3
var sq = 9
while sq <= n:
while n mod p == 0:
inc result, p
n = n div p
inc sq, (p + 1) shl 2
inc p, 2
if n > 1:
inc result, n
func primeDivisorSum(n: int): int =
var n = n
if n.isEven:
inc result, 2
n = n shr 1
while n.isEven:
n = n shr 1
var p = 3
var sq = 9
while sq <= n:
if n mod p == 0:
inc result, p
n = n div p
while n mod p == 0:
n = n div p
inc sq, (p + 1) shl 2
inc p, 2
if n > 1:
inc result, n
const Limit = 30
proc firstRuthAaronByFactors() =
echo &"First {Limit} Ruth-Aaron numbers (factors):"
var fsum1, fsum2 = 0
var n = 2
var count = 0
while count < Limit:
fsum2 = primeFactorSum(n)
if fsum1 == fsum2:
inc count
stdout.write &"{n - 1:5}", if count mod 10 == 0: '\n' else: ' '
fsum1 = fsum2
inc n
proc firstRuthAaronByDivisors() =
echo &"\nFirst {Limit} Ruth-Aaron numbers (divisors):"
var dsum1, dsum2 = 0
var n = 2
var count = 0
while count < Limit:
dsum2 = primeDivisorSum(n)
if dsum1 == dsum2:
inc count
stdout.write &"{n - 1:5}", if count mod 10 == 0: '\n' else: ' '
dsum1 = dsum2
inc n
proc firstRuthAaronTripleByFactors() =
var fsum1, fsum2 = 0
var n = 2
while true:
let fsum3 = primeFactorSum(n)
if fsum1 == fsum3 and fsum2 == fsum3:
echo &"\nFirst Ruth-Aaron triple (factors): {n - 2}"
break
fsum1 = fsum2
fsum2 = fsum3
inc n
proc firstRuthAaronTripleByDivisors() =
var dsum1, dsum2 = 0
var n = 2
while true:
let dsum3 = primeDivisorSum(n)
if dsum1 == dsum3 and dsum2 == dsum3:
echo &"\nFirst Ruth-Aaron triple (divisors): {n - 2}"
break
dsum1 = dsum2
dsum2 = dsum3
inc n
firstRuthAaronByFactors()
firstRuthAaronByDivisors()
firstRuthAaronTripleByFactors()
firstRuthAaronTripleByDivisors()

26
Task/Ruth-Aaron-numbers/Perl/ruth-aaron-numbers.pl Normal file
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#!/usr/bin/perl
use strict;
use warnings;
use ntheory qw( factor vecsum );
use List::AllUtils qw( uniq );
#use Data::Dump 'dd'; dd factor(6); exit;
my $n = 1;
my @answers;
while( @answers < 30 )
{
vecsum(factor($n)) == vecsum(factor($n+1)) and push @answers, $n;
$n++;
}
print "factors:\n\n@answers\n\n" =~ s/.{60}\K /\n/gr;
$n = 1;
@answers = ();
while( @answers < 30 )
{
vecsum(uniq factor($n)) == vecsum(uniq factor($n+1)) and push @answers, $n;
$n++;
}
print "divisors:\n\n@answers\n" =~ s/.{60}\K /\n/gr;

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Task/Ruth-Aaron-numbers/Phix/ruth-aaron-numbers.phix Normal file
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(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">ruth_aaron</span><span style="color: #0000FF;">(</span><span style="color: #004080;">bool</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">fd</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"divisors"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"factors"</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">ns</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" %d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">ss</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"s"</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">nt</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"number"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"triple"</span><span style="color: #0000FF;">)</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: #008000;">"First%s Ruth-Aaron %s%s (%s):\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">ns</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ss</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fd</span><span style="color: #0000FF;">})</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">prev</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prime_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">d</span> <span style="color: #008080;">then</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">unique</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span> <span style="color: #008080;">and</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">prev</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</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: #008000;">"%d "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</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;">if</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">prev</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span>
<span style="color: #000000;">k</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: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">ruth_aaron</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- https://oeis.org/A039752</span>
<span style="color: #000000;">ruth_aaron</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- https://oeis.org/A006145</span>
<span style="color: #000000;">ruth_aaron</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (2.1s)
-- give this one a little leg-up :-) ...</span>
<span style="color: #000000;">ruth_aaron</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">89460000</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (0.1s)
--ruth_aaron(true, 1, 3) -- (24 minutes 30s)</span>
<!--

40
Task/Ruth-Aaron-numbers/Quackery/ruth-aaron-numbers.quackery Normal file
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[ behead dup dip nested rot
witheach
[ tuck != if
[ dup dip
[ nested join ] ] ]
drop ] is -duplicates ( [ --> [ )
[ primefactors -duplicates ] is primedivisors ( n --> n )
[ 0 swap witheach + ] is sum ( [ --> n )
[ [] temp put
3 2 primefactors sum
[ over primefactors sum
tuck = if
[ over 1 -
temp take
swap join
temp put ]
dip 1+
temp share size 30 = until ]
2drop
temp take ] is raf ( --> )
[ [] temp put
3 2 primedivisors sum
[ over primedivisors sum
tuck = if
[ over 1 -
temp take
swap join
temp put ]
dip 1+
temp share size 30 = until ]
2drop
temp take ] is rad ( --> )
raf echo
cr cr
rad echo

19
Task/Ruth-Aaron-numbers/Raku/ruth-aaron-numbers.raku Normal file
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use Prime::Factor;
my @pf = lazy (^∞).hyper(:1000batch).map: *.&prime-factors.sum;
my @upf = lazy (^∞).hyper(:1000batch).map: *.&prime-factors.unique.sum;
# Task: < 1 second
put "First 30 Ruth-Aaron numbers (Factors):\n" ~
(1..∞).grep( { @pf[$_] == @pf[$_ + 1] } )[^30];
put "\nFirst 30 Ruth-Aaron numbers (Divisors):\n" ~
(1..∞).grep( { @upf[$_] == @upf[$_ + 1] } )[^30];
# Stretch: ~ 5 seconds
put "\nFirst Ruth-Aaron triple (Factors):\n" ~
(1..∞).first: { @pf[$_] == @pf[$_ + 1] == @pf[$_ + 2] }
# Really, really, _really_ slow. 186(!) minutes... but with no cheating or "leg up".
put "\nFirst Ruth-Aaron triple (Divisors):\n" ~
(1..∞).first: { @upf[$_] == @upf[$_ + 1] == @upf[$_ + 2] }

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Task/Ruth-Aaron-numbers/Sidef/ruth-aaron-numbers.sidef Normal file
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say "First 30 Ruth-Aaron numbers (factors):"
say 30.by {|n| (sopfr(n) == sopfr(n+1)) && (n > 0) }.join(' ')
say "\nFirst 30 Ruth-Aaron numbers (divisors):"
say 30.by {|n| ( sopf(n) == sopf(n+1)) && (n > 0) }.join(' ')

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Task/Ruth-Aaron-numbers/Wren/ruth-aaron-numbers.wren Normal file
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import "./math" for Int, Nums
import "./seq" for Lst
import "./fmt" for Fmt
var resF = []
var resD = []
var resT = [] // factors only
var n = 2
var factors1 = []
var factors2 = [2]
var factors3 = [3]
var sum1 = 0
var sum2 = 2
var sum3 = 3
var countF = 0
var countD = 0
var countT = 0
while (countT < 1 || countD < 30 || countF < 30) {
factors1 = factors2
factors2 = factors3
factors3 = Int.primeFactors(n+2)
sum1 = sum2
sum2 = sum3
sum3 = Nums.sum(factors3)
if (countF < 30 && sum1 == sum2) {
resF.add(n)
countF = countF + 1
}
if (sum1 == sum2 && sum2 == sum3) {
resT.add(n)
countT = countT + 1
}
if (countD < 30) {
var factors4 = factors1.toList
var factors5 = factors2.toList
Lst.prune(factors4)
Lst.prune(factors5)
if (Nums.sum(factors4) == Nums.sum(factors5)) {
resD.add(n)
countD = countD + 1
}
}
n = n + 1
}
System.print("First 30 Ruth-Aaron numbers (factors):")
System.print(resF.join(" "))
System.print("\nFirst 30 Ruth-Aaron numbers (divisors):")
System.print(resD.join(" "))
System.print("\nFirst Ruth-Aaron triple (factors):")
System.print(resT[0])
resT = [] // divisors only
n = 2
factors1 = []
factors2 = [2]
factors3 = [3]
sum1 = 0
sum2 = 2
sum3 = 3
countT = 0
while (countT < 1) {
factors1 = factors2
factors2 = factors3
factors3 = Int.primeFactors(n+2)
Lst.prune(factors3)
sum1 = sum2
sum2 = sum3
sum3 = Nums.sum(factors3)
if (sum1 == sum2 && sum2 == sum3) {
resT.add(n)
countT = countT + 1
}
n = n + 1
}
System.print("\nFirst Ruth-Aaron triple (divisors):")
System.print(resT[0])

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func DivSum(N, AllDiv); \Return sum of divisors
int N, AllDiv; \all divisors vs. only prime divisors
int F, F0, S, Q;
[F:= 2; F0:= 0; S:= 0;
repeat Q:= N/F;
if rem(0) = 0 then
[if AllDiv then S:= S+F
else if F # F0 then
[S:= S+F; F0:= F];
N:= Q;
]
else F:= F+1;
until F > N;
return S;
];
proc Ruth(AllDiv); \Show Ruth-Aaron numbers
int AllDiv;
int C, S, S0, N;
[C:= 0; S0:= 0;
N:= 2;
repeat S:= DivSum(N, AllDiv);
if S = S0 then
[IntOut(0, N-1);
C:= C+1;
if rem(C/10) = 0 then CrLf(0) else ChOut(0, ^ );
];
S0:= S;
N:= N+1;
until C >= 30;
];
[Ruth(true);
CrLf(0);
Ruth(false);
]