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A344081
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a(n) = Sum_{d|n} tau(d)^d, where tau(n) is the number of divisors of n.
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3
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1, 5, 9, 86, 33, 4109, 129, 65622, 19692, 1048613, 2049, 2176786526, 8193, 268435589, 1073741865, 152587956247, 131073, 101559956692208, 524289, 3656158441111670, 4398046511241, 17592186046469, 8388609, 4722366482871822065758
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OFFSET
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1,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 1..719
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FORMULA
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G.f.: Sum_{k >= 1} (tau(k) * x)^k/(1 - x^k).
If p is prime, a(p) = 1 + 2^p.
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MATHEMATICA
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a[n_] := DivisorSum[n, DivisorSigma[0, #]^# &]; Array[a, 24] (* Amiram Eldar, May 09 2021 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, numdiv(d)^d);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (numdiv(k)*x)^k/(1-x^k)))
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CROSSREFS
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Cf. A007425, A062367, A097988, A279789, A344047, A344080.
Sequence in context: A306123 A192202 A249937 * A171812 A221741 A344080
Adjacent sequences: A344078 A344079 A344080 * A344082 A344083 A344084
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, May 09 2021
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STATUS
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approved
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