A157195 a(n) = 0 if n is 1 or a prime, otherwise a(n) = product of the proper divisors of n.

0, 0, 0, 2, 0, 6, 0, 8, 3, 10, 0, 144, 0, 14, 15, 64, 0, 324, 0, 400, 21, 22, 0, 13824, 5, 26, 27, 784, 0, 27000, 0, 1024, 33, 34, 35, 279936, 0, 38, 39, 64000, 0, 74088, 0, 1936, 2025, 46, 0, 5308416, 7, 2500, 51, 2704, 0, 157464, 55, 175616, 57, 58, 0, 777600000

Offset: 1

Author

Jaroslav Krizek, Feb 24 2009, Feb 27 2009

Keywords

• nonn

Comments

a(n) = 0 if and only if n is a noncomposite number (cf. A008578). - Omar E. Pol, Aug 01 2012

Examples

			For n = 15 a(15) = 15 = 3*5.
		

Crossrefs

Cf. A007955, A008578, A048050.

Programs

Mathematica

If[#==1||PrimeQ[#],0,Times@@Most[Divisors[#]]]&/@Range[60] (* Harvey P. Dale, Jan 24 2014 *)

PARI

a(n) = {if ((n == 1) || isprime(n), return (0)); d = divisors(n); prod(i = 2, #d - 1, d[i]);} \\ Michel Marcus, Aug 05 2013

Python

from math import isqrt
from sympy import divisor_count
def A157195(n): return 0 if (c:=divisor_count(n)) <= 2 else (isqrt(n) if (c:=divisor_count(n)) & 1 else 1)*n**(c//2-1) # Chai Wah Wu, Jun 25 2022

Formula

a(pq) = pq, p,q = distinct primes. a(p^k) = p^((1/2*k*(k-1)), p = prime, k = integer >=2. a(c) = A007955(c)/c, c = composite number.

Extensions

Edited by N. J. A. Sloane, Mar 03 2009

Definition clarified by Harvey P. Dale, Jan 24 2014