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A308670
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a(n) = Sum_{d|n} d^(d*n).
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4
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1, 17, 19684, 4294967553, 298023223876953126, 10314424798490535546559373642, 256923577521058878088611477224235621321608, 6277101735386680763835789423207666416120802188537744130049
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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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L.g.f.: -log(Product_{k>=1} (1 - (k^k*x)^k)^(1/k)) = Sum_{k>=1} a(k)*x^k/k.
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MATHEMATICA
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a[n_] := DivisorSum[n, #^(#*n) &]; Array[a, 8] (* Amiram Eldar, May 11 2021 *)
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PROG
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(PARI) {a(n) = sumdiv(n, d, d^(d*n))}
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k^k*x)^k)^(1/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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