Data update
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Ingy döt Net
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2011 changed files with 35081 additions and 3229 deletions
51
Task/Tau-function/C-sharp/tau-function.cs
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51
Task/Tau-function/C-sharp/tau-function.cs
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internal class Program
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{
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private static void Main(string[] args)
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{
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long limit = 100;
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Console.WriteLine($"Count of divisors for the first {limit} positive integers:");
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long count = 0;
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for (long n = 1; count < limit; ++n)
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{
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Console.Write($"{DivisorCount(n),3} ");
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++count;
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if (count % 20 == 0)
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{
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Console.WriteLine();
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}
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}
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}
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private static long DivisorCount(long n)
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{
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long total = 1;
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// Deal with powers of 2 first
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for (; (n & 1) == 0; n >>= 1)
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{
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++total;
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}
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// Odd prime factors up to the square root
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for (long p = 3; p * p <= n; p += 2)
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{
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long count = 1;
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for (; n % p == 0; n /= p)
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{
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++count;
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}
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total *= count;
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}
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// If n > 1 then it's prime
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if (n > 1)
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{
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total *= 2;
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}
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return total;
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}
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}
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4
Task/Tau-function/PascalABC.NET/tau-function.pas
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4
Task/Tau-function/PascalABC.NET/tau-function.pas
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##
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function DivisorsCount(n: integer) := Range(1,n).Count(i -> n.Divs(i));
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Range(1,100).Select(n -> DivisorsCount(n)).Println
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@ -1,32 +1,42 @@
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/*REXX program counts the number of divisors (tau, or sigma_0) up to and including N.*/
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parse arg LO HI cols . /*obtain optional argument from the CL.*/
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if LO=='' | LO=="," then LO= 1 /*Not specified? Then use the default.*/
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if HI=='' | HI=="," then HI= LO + 100 - 1 /*Not specified? Then use the default.*/
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if cols=='' | cols=="," then cols= 20 /* " " " " " " */
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w= 2 + (HI>45359) /*W: used to align the output columns.*/
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say 'The number of divisors (tau) for integers up to ' n " (inclusive):"; say
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say '─index─' center(" tau (number of divisors) ", cols * (w+1) + 1, '─')
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$=; c= 0 /*$: the output list, shown ROW/line.*/
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do j=LO to HI; c= c + 1 /*list # proper divisors (tau) 1 ──► N */
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$= $ right( tau(j), w) /*add a tau number to the output list. */
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if c//cols \== 0 then iterate /*Not a multiple of ROW? Don't display.*/
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idx= j - cols + 1 /*calculate index value (for this row).*/
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say center(idx, 7) $; $= /*display partial list to the terminal.*/
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end /*j*/
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if $\=='' then say center(idx+cols, 7) $ /*there any residuals left to display ?*/
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exit 0 /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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tau: procedure; parse arg x 1 y /*X and $ are both set from the arg.*/
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if x<6 then return 2 + (x==4) - (x==1) /*some low #s should be handled special*/
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odd= x // 2 /*check if X is odd (remainder of 1).*/
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if odd then #= 2 /*Odd? Assume divisor count of 2. */
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else do; #= 4; y= x % 2; end /*Even? " " " " 4. */
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/* [↑] start with known number of divs*/
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do j=3 for x%2-3 by 1+odd while j<y /*for odd number, skip even numbers. */
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if x//j==0 then do /*if no remainder, then found a divisor*/
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#= # + 2; y= x % j /*bump # of divisors; calculate limit.*/
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if j>=y then do; #= # - 1; leave; end /*reached limit?*/
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end /* ___ */
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else if j*j>x then leave /*only divide up to √ x */
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end /*j*/; return # /* [↑] this form of DO loop is faster.*/
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/* REXX program counts the number of divisors (tau,cr sigma_0) */
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/* for a range of numbers */
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Parse Arg lo hi cols . /*obtain optional argument from the CL.*/
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If lo=='' | lo==',' Then lo=1 /*Not specified? Then use the default.*/
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If hi=='' | hi==',' Then hi=lo+100-1 /*Not specified? Then use the default.*/
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If cols=='' Then cols=20 /* " " " " " " */
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w=2+(hi>45359) /* width of columns tau(4mns5360)=100 */
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Say 'The number of divisors (tau) from' lo 'to' hi '(inclusive):'
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Say ''
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Say '-number' center(' tau (number of divisors) ',cols*(w+1)+1,'-')
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line=''
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c=0
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index=lo
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Do j=lo To hi
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c=c+1
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line=line right(tau(j),w) /* add a tau number to the output line. */
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If c//cols=0 Then Do /* line has cols numbers */
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Say center(index,7) line
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line=''
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cnt=0
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Index=index+cols
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End
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End /*j*/
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If line\=='' Then
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Say center(index,7) line /*there any residuals left To display ? */
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Exit 0 /*stick a fork in it, we're all done. */
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/*---------------------------------------------------------------------------------*/
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tau: Procedure
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Parse Arg x
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If x<6 Then /* some low numbers are handled special */
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Return 2+(x==4)-(x==1)
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tau=0
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odd=x//2
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Do j=1 by 1 While j*j<x
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If odd & j//2=0 Then /* even j can't be a divisor of an odd x*/
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Iterate
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If x//j==0 Then /* if no remainder, then found a divisor*/
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tau=tau+2 /* bump n of divisors */
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End
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If j*j=x Then /* x is a square */
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tau=tau+1 /* its root is a divisor */
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Return tau
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