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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Untouchable-numbers/REXX/untouchable-numbers.rexx Normal file
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/*REXX pgm finds N untouchable numbers (numbers that can't be equal to any aliquot sum).*/
parse arg n cols tens over . /*obtain optional arguments from the CL*/
if n='' | n=="," then n=2000 /*Not specified? Then use the default.*/
if cols='' | cols=="," | cols==0 then cols= 10 /* " " " " " " */
if tens='' | tens=="," then tens= 0 /* " " " " " " */
if over='' | over=="," then over= 20 /* " " " " " " */
tell= n>0; n= abs(n) /*N>0? Then display the untouchable #s*/
call genP n * over /*call routine to generate some primes.*/
u.= 0 /*define all possible aliquot sums ≡ 0.*/
do p=1 for #; _= @.p + 1; u._= 1 /*any prime+1 is not an untouchable.*/
_= @.p + 3; u._= 1 /* " prime+3 " " " " */
end /*p*/ /* [↑] this will also rule out 5. */
u.5= 0 /*special case as prime 2 + 3 sum to 5.*/
do j=2 for lim; if !.j then iterate /*Is J a prime? Yes, then skip it. */
y= sigmaP() /*compute: aliquot sum (sigma P) of J.*/
if y<=n then u.y= 1 /*mark Y as a touchable if in range. */
end /*j*/
call show /*maybe show untouchable #s and a count*/
if tens>0 then call powers /*Any "tens" specified? Calculate 'em.*/
exit cnt /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
genSq: do _=1 until _*_>lim; q._= _*_; end; q._= _*_; _= _+1; q._= _*_; return
grid: $= $ right( commas(t), w); if cnt//cols==0 then do; say $; $=; end; return
powers: do pr=1 for tens; call 'UNTOUCHA' -(10**pr); end /*recurse*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: #= 9; @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17; @.8=19; @.9=23 /*a list*/
!.=0; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1; !.17=1; !.19=1 !.23=1 /*primes*/
parse arg lim; call genSq /*define the (high) limit for searching*/
qq.10= 100 /*define square of the 10th prime index*/
do j=@.#+6 by 2 to lim /*find odd primes from here on forward.*/
parse var j '' -1 _; if _==5 then iterate; if j// 3==0 then iterate
if j// 7==0 then iterate; if j//11==0 then iterate; if j//13==0 then iterate
if j//17==0 then iterate; if j//19==0 then iterate; if j//23==0 then iterate
/*start dividing by the tenth prime: 29*/
do k=10 while qq.k <= j /* [↓] divide J by known odd primes.*/
if j//@.k==0 then iterate j /*J ÷ by a prime? Then ¬prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j /*bump prime count; assign a new prime.*/
!.j= 1; qq.#= j*j /*mark prime; compute square of prime.*/
end /*j*/; return /*#: is the number of primes generated*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: w=7; $= right(2, w+1) right(5, w) /*start the list of an even prime and 5*/
cnt= 2 /*count of the only two primes in list.*/
do t=6 by 2 to n; if u.t then iterate /*Is T touchable? Then skip it. */
cnt= cnt + 1; if tell then call grid /*bump count; maybe show a grid line. */
end /*t*/
if tell & $\=='' then say $ /*display a residual grid line, if any.*/
if tell then say /*show a spacing blank line for output.*/
if n>0 then say right( commas(cnt), 20) , /*indent the output a bit.*/
' untouchable numbers were found ≤ ' commas(n); return
/*──────────────────────────────────────────────────────────────────────────────────────*/
sigmaP: s= 1 /*set initial sigma sum (S) to 1. ___*/
if j//2 then do m=3 by 2 while q.m<j /*divide by odd integers up to the √ J */
if j//m==0 then s=s+m+j%m /*add the two divisors to the sum. */
end /*m*/ /* [↑] process an odd integer. ___*/
else do m=2 while q.m<j /*divide by all integers up to the √ J */
if j//m==0 then s=s+m+j%m /*add the two divisors to the sum. */
end /*m*/ /* [↑] process an even integer. ___*/
if q.m==j then return s + m /*Was J a square? If so, add √ J */
return s /* No, just return. */