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Proper divisors: Difference between revisions
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===version 2===
The following REXX version is an adaptation of the ''optimized'' version for the REXX language example for ''Factors of an integer''.
This REXX version handles all integers (negative, zero, positive) and automatically adjusts the precision (digits).
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With the (subroutine) optimization, it's over twenty times faster.
<lang rexx>/*REXX program finds proper divisors (& count) of integer ranges; & max
parse arg bot top inc range xtra
top=word(top bot 10,1); bot=word(bot 1,1); inc=word(inc 1,1)
if range=='' then range=top
w=length(top)+1; numeric digits max(9,w)
m=0
do n=bot to top by inc; q=Pdivs(n); #=words(q); if q=='∞' then #=q
say right(n,max(20,digits())) 'has' center(#,4) "proper divisors: "
end /*n*/ /* [↑] process
say; @.='and'
do r=1 for range; q=Pdivs(r); #=words(q); if #<m then iterate
@.#=@.# @. r; m=#
end /*r*/ /* [↑] process
__='is the highest number of proper divisors in range 1──►'range
say m
say /* [↓] handle any given extra numbers.
do i=1 for words(xtra); n=word(xtra,i)
numeric digits max(9,length(n)+1); q=Pdivs(n); #=words(q)
say right(n,max(20,digits())) 'has' center(#,4) "proper divisors."
end /*i*/ /* [↑]
exit /*stick a fork in it, we're all done. */
/*────────────────────────────────────────────────────────────────────────────*/
Pdivs: procedure; parse arg x,b; x=abs(x); if x==1 then return ''
odd=x//2; if x==0 then return '∞'
a=1 /* [↓]
do j=2+odd by 1+odd while j*j<x /*divide by all the integers up to √
if x//j==0 then do; a=a j; b=x%j b; end /*if ÷, add both divisors to α&ß
end /*j*/ /* [↑] % is the REXX integer division*/
/* [↓] adjust for a square.
if j*j==x then return a j b /*Was X a square? If so, add
return a b /*return the divisors (both lists). */</lang>
'''output''' when using the following input: <tt> 0 10 1 20000 166320 1441440 11796480000 </tt>
<pre>
0 has ∞ proper divisors: ∞
1 has 0 proper divisors:
2 has 1 proper divisors: 1
3 has 1 proper divisors: 1
4 has 2 proper divisors: 1 2
5 has 1 proper divisors: 1
6 has 3 proper divisors: 1 2 3
7 has 1 proper divisors: 1
8 has 3 proper divisors: 1 2 4
9 has 2 proper divisors: 1 3
10 has 3 proper divisors: 1 2 5
166320 has 159 proper divisors.
1441440 has 287 proper divisors.
</pre>
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