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Ingy döt Net 2024-07-13 15:19:22 -07:00
parent 29a5eea0d4
commit 5c1bb7bfa9
2011 changed files with 35081 additions and 3229 deletions
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59
Task/Tau-number/C-sharp/tau-number.cs Normal file
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internal class Program
{
private static void Main(string[] args)
{
long limit = 100;
Console.WriteLine($"The first {limit} tau numbers are:");
long count = 0;
for (long n = 1; count < limit; ++n)
{
if (IsTauNumber(n))
{
Console.Write($"{n, 6} ");
++count;
if (count % 10 == 0)
{
Console.WriteLine();
}
}
}
}
private static bool IsTauNumber(long n)
{
return n % DivisorCount(n) == 0;
}
private static long DivisorCount(long n)
{
long total = 1;
// Deal with powers of 2 first
for (; (n & 1) == 0; n >>= 1)
{
++total;
}
// Odd prime factors up to the square root
for (long p = 3; p * p <= n; p += 2)
{
long count = 1;
for (; n % p == 0; n /= p)
{
++count;
}
total *= count;
}
// If n > 1 then it's prime
if (n > 1)
{
total *= 2;
}
return total;
}
}

12
Task/Tau-number/PascalABC.NET/tau-number.pas Normal file
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##
function DivisorsCount(n: integer) := Range(1,n).Count(i -> n.Divs(i));
var lst := new List<integer>;
var n := 1;
while lst.Count < 100 do
begin
if n.Divs(DivisorsCount(n)) then
lst.Add(n);
n += 1;
end;
lst.Println;

81
Task/Tau-number/REXX/tau-number.rexx
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@ -1,38 +1,43 @@
/*REXX pgm displays N tau numbers, an integer divisible by the # of its divisors). */
parse arg n cols . /*obtain optional argument from the CL.*/
if n=='' | n=="," then n= 100 /*Not specified? Then use the default.*/
if cols=='' | cols=="," then cols= 10 /*Not specified? Then use the default.*/
w= max(8, length(n) ) /*W: used to align 1st output column. */
@tau= ' the first ' commas(n) " tau numbers " /*the title of the tau numbers table. */
say ' index │'center(@tau, 1 + cols*(w+1) ) /*display the title of the output table*/
say '───────┼'center("" , 1 + cols*(w+1), '─') /* " " header " " " " */
idx= 1; #= 0; $= /*idx: line; #: tau numbers; $: #s */
do j=1 until #==n /*search for N tau numbers */
if j//tau(j) \==0 then iterate /*Is this a tau number? No, then skip.*/
#= # + 1 /*bump the count of tau numbers found. */
$= $ right( commas(j), w) /*add a tau number to the output list. */
if #//cols\==0 then iterate /*Not a multiple of cols? Don't show. */
say center(idx, 7)'│' substr($, 2) /*display partial list to the terminal.*/
idx= idx + cols; $= /*bump idx by number of cols; nullify $*/
end /*j*/
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
say '───────┴'center("" , 1 + cols*(w+1), '─')
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
tau: procedure; parse arg x 1 y /*X and $ are both set from the arg.*/
if x<6 then return 2 + (x==4) - (x==1) /*some low #s should be handled special*/
odd= x // 2 /*check if X is odd (remainder of 1).*/
if odd then do; #= 2; end /*Odd? Assume divisor count of 2. */
else do; #= 4; y= x % 2; end /*Even? " " " " 4. */
/* [↑] start with known number of divs*/
do j=3 for x%2-3 by 1+odd while j<y /*for odd number, skip even numbers. */
if x//j==0 then do /*if no remainder, then found a divisor*/
#= # + 2; y= x % j /*bump # of divisors; calculate limit.*/
if j>=y then do; #= # - 1; leave; end /*reached limit?*/
end /* ___ */
else if j*j>x then leave /*only divide up to √ x */
end /*j*/ /* [↑] this form of DO loop is faster.*/
return #
/*REXX pgm displays N tau numbers (integers divisible by the # of its divisors). */
Parse Arg n cols . /*obtain optional argument from the CL. */
If n=='' | n==',' Then n= 100 /*Not specified? Then use the default. */
If cols=='' | cols==',' Then cols= 10 /*Not specified? Then use the default. */
w=6 /*W: used To align 1st output column. */
ttau=' the first ' commas(n) ' tau numbers' /* the title of the table. */
Say ' index ¦'center(ttau,cols*(w+1) ) /* display the title */
Say '-------+'center('' ,cols*(w+1),'-')
idx=1
nn=0 /* number of tau numbers */
dd=''
Do j=1 Until nn==n /* search for N tau numbers */
If j//tau(j)==0 Then Do /* If this is a tau number */
nn=nn+1 /* bump the count of tau numbers found. */
dd=dd right(commas(j),w) /* add a tau number To the output list. */
If nn//cols==0 Then Do /* a line is full */
Say center(idx,7)'¦' substr(dd,2) /* display partial list To the terminal.*/
idx= idx+cols /* bump idx by number of cols */
dd=''
End
End
End
If dd\=='' Then Say center(idx,7)'¦' substr(dd,2) /*possible display rest */
Say '--------'center('' ,cols*(w+1),'-')
Exit 0 /*stick a fork in it,we're all done. */
/*--------------------------------------------------------------------------------*/
commas: Parse Arg ?; Do jc=length(?)-3 To 1 by -3; ?=insert(',',?,jc); End; Return ?
/*--------------------------------------------------------------------------------*/
tau: Procedure
Parse Arg x
If x<6 Then /* some low numbers are handled special */
Return 2+(x==4)-(x==1)
tau=0
odd=x//2
Do j=1 by 1 While j*j<x
If odd & j//2=0 Then /* even j can't be a divisor of an odd x*/
Iterate
If x//j==0 Then /* If no remainder,Then found a divisor*/
tau=tau+2 /* bump n of divisors */
End
If j*j=x Then /* x is a square */
tau=tau+1 /* its root is a divisor */
Return tau