Perfect numbers: Difference between revisions
Content added Content deleted
m (→Lucas-Lehmer + other optimizations: add/changed comments and whitespace.) |
m (→traditional method: added/changed comments and whitespace.) |
||
| Line 1,718: | Line 1,718: | ||
:::* a ''corresponding factor'' is used when a factor is found |
:::* a ''corresponding factor'' is used when a factor is found |
||
:::* testing is stopped if the sum of the factors exceeds '''X''' |
:::* testing is stopped if the sum of the factors exceeds '''X''' |
||
<lang rexx>/*REXX program tests if a number (or a range of numbers) is/are perfect.*/ |
<lang rexx>/*REXX program tests if a number (or a range of numbers) is/are perfect. */ |
||
parse arg low high . /*obtain the specified number(s).*/ |
parse arg low high . /*obtain the specified number(s). */ |
||
if high=='' & low=='' then high=34000000 /*if no |
if high=='' & low=='' then high=34000000 /*if no arguments, then use a range. */ |
||
if low=='' then low=1 /*if no LOW, then assume unity.*/ |
if low=='' then low=1 /*if no LOW, then assume unity. */ |
||
if high=='' then high=low /*if no HIGH, then assume LOW. */ |
if high=='' then high=low /*if no HIGH, then assume LOW. */ |
||
w=length(high) /*use W for formatting output. */ |
w=length(high) /*use W for formatting the output. */ |
||
numeric digits max(9,w+2) /*ensure enough digits to handle |
numeric digits max(9,w+2) /*ensure enough digits to handle number*/ |
||
do i=low to high /*process the single number or a range.*/ |
|||
if isPerfect(i) then say right(i,w) 'is a perfect number.' |
|||
end /*i*/ |
|||
exit /*stick a fork in it, we're done.*/ |
exit /*stick a fork in it, we're all done. */ |
||
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
|||
/*──────────────────────────────────ISPERFECT subroutine────────────────*/ |
|||
isPerfect: procedure; parse arg x /* |
isPerfect: procedure; parse arg x 1 y /*obtain the number to be tested. */ |
||
if x |
if x==6 then return 1 /*handle the special case of six. */ |
||
/*[↓] perfect number's digitalRoot = 1*/ |
|||
do until y<10 /*find the digital root of Y. */ |
|||
parse var y r 2; do k=2 for length(y)-1; r=r+substr(y,k,1); end /*k*/ |
|||
y=r /*find digital root of the digit root. */ |
|||
end /*until*/ /*wash, rinse, repeat ··· */ |
|||
| ⚫ | |||
if r\==1 then return 0 /*Digital root ¬ 1? Then ¬ perfect. */ |
|||
s=1 /*the first factor of X. ___*/ |
|||
do j=2 while j*j<=x /*starting at 2, find the factors ≤√ X */ |
|||
if x//j\==0 then iterate /*J isn't a factor of X, so skip it. */ |
|||
s = s + j + x%j /*··· add it and the other factor. */ |
|||
if s>x then return 0 /*Is the sum too big? It ain't perfect*/ |
|||
| ⚫ | |||
return s==x /*if the sum matches X, it's perfect! *//</lang> |
|||
'''output''' when using the default inputs: |
'''output''' when using the default inputs: |
||
6 is a perfect number. |
6 is a perfect number. |
||