Tau number: Difference between revisions

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(→‎{{header|REXX}}: overhauled)
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=={{header|REXX}}==
=={{header|REXX}}==
Simplified, use the tau function of the respective task, ooRexx compatible
<syntaxhighlight lang="rexx">/*REXX pgm displays N tau numbers, an integer divisible by the # of its divisors). */
<syntaxhighlight lang="rexx">/*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.*/
Parse Arg n cols . /*obtain optional argument from the CL. */
if cols=='' | cols=="," then cols= 10 /*Not specified? Then use the default.*/
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. */
w=6 /*W: used To align 1st output column. */
say ' index │'center(@tau, 1 + cols*(w+1) ) /*display the title of the output table*/
ttau=' the first ' commas(n) ' tau numbers' /* the title of the table. */
say '───────┼'center("" , 1 + cols*(w+1), '─') /* " " header " " " " */
Say ' index ¦'center(ttau,cols*(w+1) ) /* display the title */
⚫
Say '-------+'center('' ,cols*(w+1),'-')
⚫
idx= 1; #= 0; $= /*idx: line; #: tau numbers; $: #s */
idx=1
⚫
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.*/
nn=0 /* number of tau numbers */
dd=''
⚫
#= # + 1 /*bump the count of tau numbers found. */
$= $ right( commas(j), w) /*add a tau number to the output list. */
Do j=1 Until nn==n /* search for N tau numbers */
if #//cols\==0 then iterate /*Not a multiple of cols? Don't show. */
If j//tau(j)==0 Then Do /* If this is a tau number */
say center(idx, 7)'│' substr($, 2) /*display partial list to the terminal.*/
nn=nn+1 /* bump the count of tau numbers found. */
idx= idx + cols; $= /*bump idx by number of cols; nullify $*/
dd=dd right(commas(j),w) /* add a tau number To the output list. */
end /*j*/
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 */
⚫
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
dd=''
⚫
say '───────┴'center("" , 1 + cols*(w+1), '─')
End
exit 0 /*stick a fork in it, we're all done. */
End
/*──────────────────────────────────────────────────────────────────────────────────────*/
End
⚫
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
If dd\=='' Then Say center(idx,7)'¦' substr(dd,2) /*possible display rest */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Say '--------'center('' ,cols*(w+1),'-')
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*/
Exit 0 /*stick a fork in it,we're all done. */
/*--------------------------------------------------------------------------------*/
⚫
odd= x // 2 /*check if X is odd (remainder of 1).*/
⚫
commas: Parse Arg ?; Do jc=length(?)-3 To 1 by -3; ?=insert(',',?,jc); End; Return ?
if odd then do; #= 2; end /*Odd? Assume divisor count of 2. */
/*--------------------------------------------------------------------------------*/
else do; #= 4; y= x % 2; end /*Even? " " " " 4. */
tau: Procedure
/* [↑] start with known number of divs*/
Parse Arg x
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*/
If x<6 Then /* some low numbers are handled special */
Return 2+(x==4)-(x==1)
#= # + 2; y= x % j /*bump # of divisors; calculate limit.*/
tau=0
if j>=y then do; #= # - 1; leave; end /*reached limit?*/
odd=x//2
end /* ___ */
Do j=1 by 1 While j*j<x
else if j*j>x then leave /*only divide up to √ x */
end /*j*/ /* [↑] this form of DO loop is faster.*/
If odd & j//2=0 Then /* even j can't be a divisor of an odd x*/
Iterate
⚫
return #</syntaxhighlight>
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 </syntaxhighlight>
{{out|output|text=&nbsp; when using the default input:}}
{{out|output|text=&nbsp; when using the default input:}}
<pre>
<pre>
index │ the first 100 tau numbers
index ¦ the first 100 tau numbers
-------+----------------------------------------------------------------------
───────┼───────────────────────────────────────────────────────────────────────────────────────────
1 │ 1 2 8 9 12 18 24 36 40 56
1 ¦ 1 2 8 9 12 18 24 36 40 56
11 │ 60 72 80 84 88 96 104 108 128 132
11 ¦ 60 72 80 84 88 96 104 108 128 132
21 │ 136 152 156 180 184 204 225 228 232 240
21 ¦ 136 152 156 180 184 204 225 228 232 240
31 │ 248 252 276 288 296 328 344 348 360 372
31 ¦ 248 252 276 288 296 328 344 348 360 372
41 │ 376 384 396 424 441 444 448 450 468 472
41 ¦ 376 384 396 424 441 444 448 450 468 472
51 │ 480 488 492 504 516 536 560 564 568 584
51 ¦ 480 488 492 504 516 536 560 564 568 584
61 │ 600 612 625 632 636 640 664 672 684 708
61 ¦ 600 612 625 632 636 640 664 672 684 708
71 │ 712 720 732 776 792 804 808 824 828 852
71 ¦ 712 720 732 776 792 804 808 824 828 852
81 │ 856 864 872 876 880 882 896 904 936 948
81 ¦ 856 864 872 876 880 882 896 904 936 948
91 │ 972 996 1,016 1,040 1,044 1,048 1,056 1,068 1,089 1,096
91 ¦ 972 996 1,016 1,040 1,044 1,048 1,056 1,068 1,089 1,096
------------------------------------------------------------------------------</pre>
───────┴───────────────────────────────────────────────────────────────────────────────────────────
</pre>


=={{header|Ring}}==
=={{header|Ring}}==
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