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Abundant odd numbers: Difference between revisions

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Abundant odd numbers (view source)

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→‎{{header|REXX}}: ooRexx conformance and only one loop instead of three
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(→‎{{header|REXX}}: ooRexx conformance and only one loop instead of three)
 
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The   '''sigO'''   function is a specialized version of the   '''sigma'''   function optimized just for   ''odd''   numbers.
<syntaxhighlight lang="rexx">/*REXX pgm displays abundant odd numbers: 1st 25, one─thousandthone-thousandth, first > 1 billion. */
parse arg Nlow Nuno Novr . /*obtain optional arguments from the CL*/
if Nlow=='' | Nlow=="',"' then Nlow= 25 /*Not specified? Then use the default.*/
if Nuno=='' | Nuno=="',"' then Nuno= 1000 /* "' "' "' "' "' "' */
if Novr=='' | Novr=="',"' then Novr= 1000000000 /* "' "' "' "' "' "' */
numeric digits max(9, length(Novr) ) /*ensure enough decimal digits for // */
@a= 'odd abundant number' /*variable for annotating the output. */
#n= 0 /*count of odd abundant numbers so far.*/
do j=3 by 2 until #n>=Nlow; $= sigO(j) /*get the sigma for an odd integer. */
d=sigO(j)
if $<=j then iterate /*sigma ≤ J ? Then ignore it. */▼
if d>j then Do #= # + 1 /*sigma = J ? Then ignore it. /*bump the counter for abundant odd #'s*/
n= n say+ rt(th(#))1 @ 'is:'rt(commas(j), 8) rt("sigma=") rt(commas($), 9) /*bump the counter for abundant odd n's*/
say rt(th(n)) a 'is:'rt(commas(j),8) rt('sigma=') rt(commas(d),9)
end /*j*/▼
End
▲ end /*j*/
say
#n= 0 /*count of odd abundant numbers so far.*/
do j=3 by 2; $= sigO(j) /*get the sigma for an odd integer. */
d= sigO(j)
if $<=j then iterate /*sigma ≤ J ? Then ignore it. */▼
if d>j #= #then +do 1 /*sigma = J ? Then ignore it. /*bump the counter for abundant odd #'s*/
 
if #<Nuno then iterate /*Odd abundant# count<Nuno? Then skip.*/
n= n say+ rt(th(#))1 @ 'is:'rt(commas(j), 8) rt("sigma=") rt(commas($), 9) /*bump the counter for abundant odd n's*/
▲ if $<n>=jNuno then iteratedo /*sigma ≤ /*Odd Jabundantn count<Nuno? Then ignore itskip. */
say rt(th(n)) a 'is:'rt(commas(j),8) rt('sigma=') rt(commas(d),9)
leave /*we're finished displaying NUNOth num.*/
end /*j*/End
End
end /*j*/▼
say
do j=1+Novr%2*2 by 2; $= sigO(j) /*get sigma for an odd integer > Novr. */
d= sigO(j)
if $<=j then iterate /*sigma ≤ J ? Then ignore it. */
if d>j say rt(th(1))then Do @ 'over' commas(Novr) "is: " commas(j) rt(' /*sigma =') commas($)J ? Then ignore it. */
say rt(th(1)) a 'over' commas(Novr) 'is: ' commas(j) rt('sigma=') commas(d)
leaveLeave /*we're finished displaying NOVRth num.*/
▲ end /*j*/
End
exit /*stick a fork in it, we're all done. */
end /*j*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
exit
commas:parse arg _; do c_=length(_)-3 to 1 by -3; _=insert(',', _, c_); end; return _▼
/*--------------------------------------------------------------------------------------*/
rt: procedure; parse arg #,len; if len=='' then len= 20; return right(#, len)▼
▲commas:parse arg _; do c_=length(_)-3 to 1 by -3; _=insert(',', _, c_); end; return _
th: parse arg th; return th||word('th st nd rd',1+(th//10)*(th//100%10\==1)*(th//10<4))▼
▲rt: procedure; parse arg #n,len; if len=='' then len= 20; return right(#n, len)
/*──────────────────────────────────────────────────────────────────────────────────────*/
▲th: parse arg th; return th||word('th st nd rd',1+(th//10)*(th//100%10\==1)*(th//10<4))
sigO: parse arg x; s= 1 /*sigma for odd integers. ___*/
/*--------------------------------------------------------------------------------------*/
do k=3 by 2 while k*k<x /*divide by all odd integers up to √ x */
sigO: parse arg x; if x//k==0 then s= s + k + x%k /*addsigma for odd integers. the two divisors to (sigma) sum. ___*/
s=1
end /*k*/ /* ___*/
do k=3 by 2 ifwhile k*k==<x then return s + k /*Was X a square? divide by all Ifodd so,integers addup to √v x */
if x//k==0 then
return s /*return (sigma) sum of the divisors. */</syntaxhighlight>▼
s= s + k + x%k /*add the two divisors to (sigma) sum. */
▲ end if $<=j/*k*/ then iterate /*sigma ≤ J ? Then ignore it. ___*/
if k*k==x then
return s + k /*Was X a square? If so,add v x */
▲ return s /*return (sigma) sum of the divisors. */</syntaxhighlight>
</syntaxhighlight>
{{out|output|text=&nbsp; when using the default input:}}
<pre>
Walterpachl
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