OFFSET
1,4
COMMENTS
a(n) = 0 if and only if n is a noncomposite number (cf. A008578). - Omar E. Pol, Aug 01 2012
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
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