Data update
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Ingy döt Net
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2347 changed files with 62432 additions and 16731 deletions
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/*REXX pgm finds N untouchable numbers (numbers that can't be equal to any aliquot sum).*/
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parse arg n cols tens over . /*obtain optional arguments from the CL*/
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if n='' | n=="," then n=2000 /*Not specified? Then use the default.*/
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if cols='' | cols=="," | cols==0 then cols= 10 /* " " " " " " */
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if tens='' | tens=="," then tens= 0 /* " " " " " " */
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if over='' | over=="," then over= 20 /* " " " " " " */
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tell= n>0; n= abs(n) /*N>0? Then display the untouchable #s*/
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call genP n * over /*call routine to generate some primes.*/
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u.= 0 /*define all possible aliquot sums ≡ 0.*/
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do p=1 for #; _= @.p + 1; u._= 1 /*any prime+1 is not an untouchable.*/
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_= @.p + 3; u._= 1 /* " prime+3 " " " " */
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end /*p*/ /* [↑] this will also rule out 5. */
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u.5= 0 /*special case as prime 2 + 3 sum to 5.*/
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do j=2 for lim; if !.j then iterate /*Is J a prime? Yes, then skip it. */
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y= sigmaP() /*compute: aliquot sum (sigma P) of J.*/
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if y<=n then u.y= 1 /*mark Y as a touchable if in range. */
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end /*j*/
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call show /*maybe show untouchable #s and a count*/
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if tens>0 then call powers /*Any "tens" specified? Calculate 'em.*/
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exit cnt /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
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genSq: do _=1 until _*_>lim; q._= _*_; end; q._= _*_; _= _+1; q._= _*_; return
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grid: $= $ right( commas(t), w); if cnt//cols==0 then do; say $; $=; end; return
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powers: do pr=1 for tens; call 'UNTOUCHA' -(10**pr); end /*recurse*/; return
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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genP: #= 9; @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17; @.8=19; @.9=23 /*a list*/
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!.=0; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1; !.17=1; !.19=1 !.23=1 /*primes*/
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parse arg lim; call genSq /*define the (high) limit for searching*/
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qq.10= 100 /*define square of the 10th prime index*/
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do j=@.#+6 by 2 to lim /*find odd primes from here on forward.*/
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parse var j '' -1 _; if _==5 then iterate; if j// 3==0 then iterate
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if j// 7==0 then iterate; if j//11==0 then iterate; if j//13==0 then iterate
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if j//17==0 then iterate; if j//19==0 then iterate; if j//23==0 then iterate
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/*start dividing by the tenth prime: 29*/
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do k=10 while qq.k <= j /* [↓] divide J by known odd primes.*/
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if j//@.k==0 then iterate j /*J ÷ by a prime? Then ¬prime. ___ */
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end /*k*/ /* [↑] only process numbers ≤ √ J */
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#= #+1; @.#= j /*bump prime count; assign a new prime.*/
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!.j= 1; qq.#= j*j /*mark prime; compute square of prime.*/
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end /*j*/; return /*#: is the number of primes generated*/
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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show: w=7; $= right(2, w+1) right(5, w) /*start the list of an even prime and 5*/
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cnt= 2 /*count of the only two primes in list.*/
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do t=6 by 2 to n; if u.t then iterate /*Is T touchable? Then skip it. */
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cnt= cnt + 1; if tell then call grid /*bump count; maybe show a grid line. */
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end /*t*/
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if tell & $\=='' then say $ /*display a residual grid line, if any.*/
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if tell then say /*show a spacing blank line for output.*/
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if n>0 then say right( commas(cnt), 20) , /*indent the output a bit.*/
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' untouchable numbers were found ≤ ' commas(n); return
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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sigmaP: s= 1 /*set initial sigma sum (S) to 1. ___*/
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if j//2 then do m=3 by 2 while q.m<j /*divide by odd integers up to the √ J */
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if j//m==0 then s=s+m+j%m /*add the two divisors to the sum. */
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end /*m*/ /* [↑] process an odd integer. ___*/
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else do m=2 while q.m<j /*divide by all integers up to the √ J */
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if j//m==0 then s=s+m+j%m /*add the two divisors to the sum. */
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end /*m*/ /* [↑] process an even integer. ___*/
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if q.m==j then return s + m /*Was J a square? If so, add √ J */
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return s /* No, just return. */
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-- 8 May 2025
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include Settings
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say 'UNTOUCHABLE NUMBERS'
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say version
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say
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xx = 2000; yy = 8*xx
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call GetPrimes yy
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call MarkTouchables xx,yy
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call DisplayList xx
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xx = 100000; yy = 14*xx
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call GetPrimes yy
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call MarkTouchables xx,yy
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call DisplayCount xx
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call Timer
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exit
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GetPrimes:
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procedure expose prim. flag.
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arg yy
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say 'Get primes below' yy'...'
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say Primes(yy) 'found'
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say
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return
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MarkTouchables:
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procedure expose touc. prim. flag.
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arg xx,yy
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say 'Mark touchable numbers below' xx'...'
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touc. = 0
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do p = 1 to prim.0
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a = prim.p+1; touc.a = 1
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a = prim.p+3; touc.a = 1
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end
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touc.5 = 0
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do j = 2 for yy
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if flag.j then
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iterate j
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y = Aliquot(j)
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if y <= xx then
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touc.y = 1
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end
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say 'Done'
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say
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return
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DisplayList:
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procedure expose touc.
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arg xx
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say 'Show untouchable numbers below' xx'...'
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n = 2
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call Charout ,Right(2,5) Right(5,4)
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do i = 6 by 2 to xx
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if touc.i then
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iterate i
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n = n+1
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call Charout ,Right(i,5)
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if n//10 = 0 then
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say
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end
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say
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say n 'found'
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say
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return
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DisplayCount:
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procedure expose touc.
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arg xx
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say 'Show untouchable number count...'
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n = 2; a = 10
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do i = 6 by 2 to xx+10
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if touc.i then
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iterate i
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if i > a then do
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say right(n,5) 'below' right(a,6)
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a = a*10
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end
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n = n+1
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end
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say
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return
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include Sequences
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include Helper
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include Functions
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include Special
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include Constants
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include Abend
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