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A338689
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a(n) = Sum_{d|n} (-1)^(d-1) * (n/d)^n * binomial(d+n/d-2, d-1).
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2
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1, 3, 28, 223, 3126, 44660, 823544, 16514047, 387538588, 9951176994, 285311670612, 8903202187413, 302875106592254, 11107259264162760, 437894348359764856, 18444492187995996159, 827240261886336764178, 39345059356329821149097
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} (k * x/(1 + (k * x)^k))^k.
If p is prime, a(p) = (-1)^(p-1) + p^p.
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MATHEMATICA
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a[n_] := DivisorSum[n, (-1)^(# - 1) * (n/#)^n * Binomial[# + n/# - 2, # - 1] &]; Array[a, 20] (* Amiram Eldar, Apr 24 2021 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, (-1)^(d-1)*(n/d)^n*binomial(d+n/d-2, d-1));
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, (k*x/(1+(k*x)^k))^k))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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