A157721 a(n) = 0 if n is 1 or a prime, otherwise a(n) = product of composite (nonprime) divisors of n.

0, 0, 0, 4, 0, 6, 0, 32, 9, 10, 0, 288, 0, 14, 15, 512, 0, 972, 0, 800, 21, 22, 0, 55296, 25, 26, 243, 1568, 0, 27000, 0, 16384, 33, 34, 35, 1679616, 0, 38, 39, 256000, 0, 74088, 0, 3872, 6075, 46, 0, 42467328, 49, 12500, 51, 5408, 0, 1417176, 55, 702464, 57, 58, 0

Offset: 1

Author

Jaroslav Krizek, Mar 04 2009

Keywords

• nonn
• look

Comments

a(n) = 0 if n = 1 or n is prime; a(n) = n if n is semiprime (A001358). a(c) = A007955(c) / A007947(c) = (c^(A000005(c)/2)) / A007947(c) = A087652(c), for c = composite numbers (A002808). a(p) = A087652(p) - 1 = 0, for p = primes (A000040).

Examples

			a(12) = 4*6*12 = 288, composite divisors = {4,6,12}.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007955, A007947, A000005, A087652, A002808, A000040.

Programs

Maple

f:= proc(n) if isprime(n) then 0 else convert(remove(isprime,numtheory:-divisors(n)),`*`) fi end proc;
f(1):= 0:
map(f, [$1..100]); # Robert Israel, Jul 31 2024

Mathematica

f[n_] := If[n == 1 || PrimeQ@n, 0, Times @@ Select[Divisors@n, ! PrimeQ@# &]]; Array[f, 60] (* Robert G. Wilson v, May 04 2009 *)

Extensions

More terms from Robert G. Wilson v, May 04 2009