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A188902
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Numerator of the base n logarithm of the product of the divisors of n.
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1
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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, 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, 4, 1, 6, 1, 2, 3, 3, 2
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OFFSET
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2,3
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COMMENTS
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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.
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LINKS
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FORMULA
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MATHEMATICA
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Numerator[Table[FullSimplify[Log[n, Times@@Divisors[n]]], {n, 2, 75}]]
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PROG
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(Python)
from sympy import divisor_count, Integer
def a(n): return (divisor_count(n) / 2).numerator()
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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STATUS
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approved
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