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A308753
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a(n) = Sum_{d|n} d^(2*(d-1)).
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4
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1, 5, 82, 4101, 390626, 60466262, 13841287202, 4398046515205, 1853020188851923, 1000000000000390630, 672749994932560009202, 552061438912436478063702, 542800770374370512771595362, 629983141281877223617054459942
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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 - x^k)^(k^(2*k-3))) = Sum_{k>=1} a(k)*x^k/k.
G.f.: Sum_{k>=1} k^(2*(k-1)) * x^k/(1 - x^k).
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MATHEMATICA
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a[n_] := DivisorSum[n, #^(2*(# - 1)) &]; Array[a, 14] (* Amiram Eldar, May 08 2021 *)
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PROG
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(PARI) {a(n) = sumdiv(n, d, d^(2*(d-1)))}
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(2*k-3)))))
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(2*(k-1))*x^k/(1-x^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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