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=={{header|REXX}}==
Simplified, use the tau function of the respective task, ooRexx compatible
<syntaxhighlight lang="rexx">/*REXX pgm displays N tau numbers, an integer(integers divisible by the # of its divisors). */
parse arg n cols . /*obtain optional argument from the CL.*/
ifParse Arg n cols . n=='' | n=="," then n= 100 /*Notobtain specified?optional argument Then usefrom the defaultCL. */
ifIf cols n=='' | cols=="," then colsn==',' 10 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. */
@tauw=6 ' the first ' commas(n) " tau numbers " /*theW: titleused ofTo thealign tau1st numbersoutput tablecolumn. */
say ttau=' indexthe first │'center(@tau, 1 + cols*commas(w+1n) ' tau )numbers' /*display the title of the output table. */
saySay '───────┼ index ¦'center("" ttau, 1 + cols*(w+1), '─') /* ") /* display the title " header " " " " */
saySay ' ───────┴-------+'center( ""'' , 1 + cols*(w+1), ' ─-') ▼idx= 1; #= 0; $= /*idx: line; #: tau numbers; $: #s */ ▼idx=1
do j=1 until #==n /*search for N tau numbers */ ▼nn=0 if j//tau(j) \==0 then iterate /*Is thisnumber aof tau number?numbers No, then skip.*/
dd=''
#= # + 1 /*bump the count of tau numbers found. */ ▼Do j=1 Until nn==n $= $ right( commas(j), w) /*add asearch for N tau numbernumbers to the output list. */
If j//tau(j)==0 Then Do if #//cols\==0 then iterate /* If this /*Notis a multipletau number of cols? Don't show. */
nn=nn+1 say center(idx, 7)'│' substr($, 2) /*display partialbump listthe tocount theof terminaltau numbers found. */
idxdd=dd idxright(commas(j),w) + cols; $= /*bump idxadd bya tau number ofTo the cols;output nullifylist. $*/
If nn//cols==0 Then Do end /*j a line is full */
if $\=='' then say Say center(idx, 7) "│" '¦' substr( $dd, 2) /* possible display residualpartial list To the outputterminal.*/ ▼
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.*/
Exit 0 if x<6 then return 2 + (x==4) - (x==1) /*somestick a fork in it,we're lowall #sdone. should be handled special*/
/*--------------------------------------------------------------------------------*/
▲ odd= x // 2 /*check if X is odd (remainder of 1).*/
▲commas: parseParse argArg ?; doDo jc=length(?)-3 toTo 1 by -3; ?=insert(',', ?, jc); endEnd; returnReturn ?
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<6 Then if x//j==0 then do /*if nosome low remainder,numbers thenare foundhandled aspecial divisor*/
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 */
If odd & end j/*j*/2=0 Then /* even j can't be a /* [↑] this formdivisor of DO loopan isodd faster.x*/
Iterate
return #</syntaxhighlight> ▼ If x//j==0 Then /* If no remainder,Then found a divisor*/
▲ tau=tau+2 do j=1 until #==n /* search forbump n of divisors N tau numbers */
End
▲idx If j*j= x 1;Then #= 0; /* x is a square $= /*idx: line; #: tau numbers; $: #s */
▲ tau=tau+1 #= # + 1 /* its root is a divisor /*bump the count of tau numbers found. */
▲ Return tau return #</syntaxhighlight>
{{out|output|text= when using the default input:}}
<pre>
index │ ¦ the first 100 tau numbers
-------+----------------------------------------------------------------------
───────┼───────────────────────────────────────────────────────────────────────────────────────────
1 │ ¦ 1 2 8 9 12 18 24 36 40 56
11 │ ¦ 60 72 80 84 88 96 104 108 128 132
21 │ ¦ 136 152 156 180 184 204 225 228 232 240
31 │ ¦ 248 252 276 288 296 328 344 348 360 372
41 │ ¦ 376 384 396 424 441 444 448 450 468 472
51 │ ¦ 480 488 492 504 516 536 560 564 568 584
61 │ ¦ 600 612 625 632 636 640 664 672 684 708
71 │ ¦ 712 720 732 776 792 804 808 824 828 852
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
------------------------------------------------------------------------------</pre>
───────┴───────────────────────────────────────────────────────────────────────────────────────────
</pre>
=={{header|Ring}}==
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