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%I #28 May 07 2020 16:30:46
%S 1,1,3,1,2,1,2,3,2,1,3,1,2,2,5,1,3,1,3,2,2,1,4,3,2,2,3,1,4,1,3,2,2,2,
%T 9,1,2,2,4,1,4,1,3,3,2,1,5,3,3,2,3,1,4,2,4,2,2,1,6,1,2,3,7,2,4,1,3,2,
%U 4,1,6,1,2,3,3,2
%N Numerator of the base n logarithm of the product of the divisors of n.
%C 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.
%C a(1) is of course indeterminate since it can be any value desired, whether real, imaginary or complex.
%C The denominator is A010052(n) + 1.
%H Antti Karttunen, <a href="/A188902/b188902.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = numerator(A000005(n)/2).
%F a(n) = (A038548(n) + A056924(n)) / 2 for n > 1.
%t Numerator[Table[FullSimplify[Log[n, Times@@Divisors[n]]], {n, 2, 75}]]
%o (PARI) A188902(n) = numerator(numdiv(n)/2); \\ _Antti Karttunen_, May 27 2017
%o (Python)
%o from sympy import divisor_count, Integer
%o def a(n): return (divisor_count(n) / 2).numerator()
%o print([a(n) for n in range(2, 51)]) # _Indranil Ghosh_, May 27 2017
%Y Cf. A000005, A007955, A007956, A038548, A056924, A010052.
%K nonn,easy,frac
%O 2,3
%A _Alonso del Arte_, Apr 19 2011
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