OFFSET
2,3
COMMENTS
Obviously the product of divisors of n (see A007955) is a multiple of n. But often it is also a perfect power of n, a number of the form n^m with m an integer. But if n is a perfect square (A000290), then the logarithm is a rational number but not an integer.
a(1) is of course indeterminate since it can be any value desired, whether real, imaginary or complex.
The denominator is A010052(n) + 1.
LINKS
Antti Karttunen, Table of n, a(n) for n = 2..10000
MATHEMATICA
Numerator[Table[FullSimplify[Log[n, Times@@Divisors[n]]], {n, 2, 75}]]
PROG
(PARI) A188902(n) = numerator(numdiv(n)/2); \\ Antti Karttunen, May 27 2017
(Python)
from sympy import divisor_count, Integer
def a(n): return (divisor_count(n) / 2).numerator()
print([a(n) for n in range(2, 51)]) # Indranil Ghosh, May 27 2017
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Alonso del Arte, Apr 19 2011
STATUS
approved