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Anti-primes: Difference between revisions
→{{header|REXX}}: added the REXX computer programming language.
(→{{header|zkl}}: added code) |
(→{{header|REXX}}: added the REXX computer programming language.) |
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{{out}}
<pre>[1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560]</pre>
=={{header|REXX}}==
This REXX version is using a modified version of a highly optimized ''proper divisors'' function.
<lang rexx>/*REXX program finds N number of anti─primes or highly─composite numbers. */
parse arg N . /*obtain optional argument from the CL.*/
if N=='' | N=="," then N=20 /*Not specified? Then use the default.*/
maxD= 0 /*the maximum number of divisors so far*/
#= 0 /*the count of anti─primes found " " */
$= /*the list of anti─primes found " " */
do k=1 until #==N; d= #divs(k) /*obtain the number of divisors for K.*/
if d<=maxD then iterate /*Is D ≤ previous div count? Skip it. */
#= # + 1; $= $ k /*found an anti1prime #, add it to list*/
maxD= d /*use this as the new high─water mark. */
end /*k*/
say
say 'The first ' N " anti─primes (highly─composite numbers) are:"
say strip($)
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
#divs: procedure; parse arg x 1 y /*X and Y: both set from 1st argument.*/
if x<3 then return x /*handle special case for one and two. */
if x==4 then return 3 /* " " " " four. */
if x<6 then return 2 /* " " " " three or five*/
odd= x // 2 /*check if X is odd or not. */
if odd then do; #= 1; end /*Odd? Assume Pdivisors count of 1.*/
else do; #= 3; y= x%2; end /*Even? " " " " 3.*/
/* [↑] start with known num of Pdivs.*/
do j=3 for x%2-3 by 1+odd while j<y /*for odd numbers, skip evens.*/
if x//j==0 then do /*if no remainder, then found a divisor*/
#=#+2; y=x%j /*bump # Pdivs, calculate limit Y. */
if j>=y then do; #= #-1; leave; end /*limit?*/
end /* ___ */
else if j*j>x then leave /*only divide up to √ x */
end /*j*/ /* [↑] this form of DO loop is faster.*/
return #+1 /*bump "proper divisors" to "divisors".*/</lang>
{{out|output|text= when using the default input of: <tt> 20 </tt>}}
<pre>
The first 20 anti─primes (highly─composite numbers) are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560
</pre>
=={{header|Sidef}}==
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