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

1,4

Comments

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

Links

Table of n, a(n) for n=1..60.

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007955, A008578, A048050.

Sequence in context: A353276 A046520 A146076 * A019781 A335959 A167294

Adjacent sequences: A157192 A157193 A157194 * A157196 A157197 A157198

Keyword

nonn

Author

Jaroslav Krizek, Feb 24 2009, Feb 27 2009

Extensions

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

Definition clarified by Harvey P. Dale, Jan 24 2014

Status

approved