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

1,4

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).

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A075091 A132953 A195207 * A085968 A353005 A010637

Adjacent sequences: A157718 A157719 A157720 * A157722 A157723 A157724

Keyword

nonn,look

Author

Jaroslav Krizek, Mar 04 2009

Extensions

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

Status

approved