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

1,4

Links

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A197008 A344442 A316223 * A381885 A072195 A032310

Adjacent sequences: A087649 A087650 A087651 * A087653 A087654 A087655

Keyword

nonn

Author

Reinhard Zumkeller, Sep 25 2003

Status

approved