A087652 Product of the nonprime divisors of n.

1, 1, 1, 4, 1, 6, 1, 32, 9, 10, 1, 288, 1, 14, 15, 512, 1, 972, 1, 800, 21, 22, 1, 55296, 25, 26, 243, 1568, 1, 27000, 1, 16384, 33, 34, 35, 1679616, 1, 38, 39, 256000, 1, 74088, 1, 3872, 6075, 46, 1, 42467328, 49, 12500, 51, 5408, 1, 1417176, 55, 702464, 57, 58

Offset: 1

Author

Reinhard Zumkeller, Sep 25 2003

Keywords

• nonn

Examples

			For n = 12: nonprime divisors = {4,6,12}: a(12) = 4*6*12 = 288.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A001358, A007947, A007955, A023890, A033273.

Programs

Mathematica

a[n_] := n^(DivisorSigma[0, n]/2) / Times @@ FactorInteger[n][[;;, 1]]; Array[a, 100] (* Amiram Eldar, Feb 01 2025 *)

PARI

a(n) = my(p=1); fordiv(n, d, if (!isprime(d), p*=d)); p; \\ Michel Marcus, Aug 05 2017

Formula

a(n) = 1 if n = 1 or n is prime.

a(n) = n if n = 1 or n is semiprime (A001358).

From Wesley Ivan Hurt, Jun 08 2020: (Start)

a(n) = Product_{d|n, d nonprime} d.

If n is squarefree, then a(n) = n^(d(n)/2-1), where d(n) is the number of divisors of n (A000005). (End)

a(p^e) = p^((e^2+e-2)/2) for p prime, e > 0. - Bernard Schott, Jun 08 2020

a(n) = A007955(n)/A007947(n). - Amiram Eldar, Feb 01 2025