Proper divisors: Difference between revisions

<lang rexx>/*REXX pgmprogram finds proper divisors (& count) of some integer ranges,; max of #s. maximum*/

parse arg lowbot hightop inc range xtra /*get optional args from C.L. */

hightop=word(hightop lowbot 10,1); lowbot=word(lowbot 1,1); inc=word(inc 1,1) /*opts1st range*/

if range=='' then range=high top /*use HIGH TOP for the 2nd range.*/

w=length(hightop)+1; numeric digits max(9,w) /*'nuff digs for // operation*/

do n=lowbot to hightop by inc; q=Pdivs(n); #=words(q); if q=='∞' then #=q

say right(n,digits()) 'has' center(#,4) "proper divisors: " q

end /*n*/ /* [↑] process a range of intsintegers. */

do r@.#=1@.# for@. range; q=Pdivs(r); #=words(q); if m=#<m then iterate

say /* [↓] handle any given extra numbers. */

do i=1 for words(xtra); n=word(xtra,i); w=length(n)+1

numeric digits max(9,wlength(n)+1); q=Pdivs(n); #=words(q)

end /*i*/ /* [↑] support extra given numsintegers. */

exit /*stick a fork in it, we're all done. */

/*──────────────────────────────────PDIVS subroutine────────────────────subroutine──────────────────────────*/

odd=x//2; if x==0 then return 'infinite∞'; odd=x//2

a=1 /* [↓] use process only EVEN|ODDEVEN│ODD integers.*/

do j=2+odd by 1+odd while j*j<x /*divide by all integers up to √x. */

if x//j==0 then do; a=a j; b=x%j b; end /*add divsdivisors to α&ß lists if ÷*/

end /*j*/ /* [↑] % is the REXX integer dividedivision*/

/* [↓] adjust for square. _ */

if j*j==x then return a j b /*Was X a square? If so, add √x. */

return a b /*return the divisors (both lists). */</lang>

'''output''' when using the following input: &nbsp; <tt> 10 &nbsp; 10 &nbsp; 1 &nbsp; &nbsp; &nbsp; 20000 &nbsp; &nbsp; &nbsp; 166320 &nbsp; 1441440 &nbsp; 11796480000 </tt>