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A302974
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a(n) = numerator of tau(n)^n / n^tau(n).
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3
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1, 1, 8, 81, 32, 256, 128, 16, 27, 65536, 2048, 729, 8192, 16777216, 1073741824, 152587890625, 131072, 2985984, 524288, 892616806656, 4398046511104, 1099511627776, 8388608, 281474976710656, 847288609443, 281474976710656, 18014398509481984, 1499253470328324096
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OFFSET
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1,3
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COMMENTS
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tau(n) = the number of the divisors of n (A000005).
a(n) <= A302975(n) only for numbers n = 1, 2 and 3.
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LINKS
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EXAMPLE
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For n = 6; tau(6)^6 / 6^tau(6) = 4^6 / 6^4 = 256 / 81; a(6) = 256.
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MATHEMATICA
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Numerator[#[[2]]^#[[1]]/#[[1]]^#[[2]]]&/@Table[{n, DivisorSigma[0, n]}, {n, 30}] (* Harvey P. Dale, May 29 2023 *)
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PROG
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(Magma) [Numerator((NumberOfDivisors(n)^n) / (n^NumberOfDivisors(n))): n in[1..100]]
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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