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A308688
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a(n) = Sum_{d|n} d^(2*n/d - 1).
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4
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1, 3, 4, 13, 6, 66, 8, 201, 253, 648, 12, 5488, 14, 8550, 22824, 49681, 18, 316743, 20, 865578, 1611152, 2098506, 24, 27246276, 1953151, 33556656, 129199240, 202152908, 30, 1758141606, 32, 3223326753, 10460514288, 8589939540, 1261056768, 146050621105, 38
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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^2*x^k)^(1/k^2)) = Sum_{k>=1} a(k)*x^k/k.
a(p) = p+1 for prime p.
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MATHEMATICA
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a[n_] := DivisorSum[n, #^(2*n/# - 1) &]; Array[a, 37] (* Amiram Eldar, May 09 2021 *)
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PROG
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(PARI) {a(n) = sumdiv(n, d, d^(2*n/d-1))}
(PARI) N=66; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k^2*x^k)^(1/k^2)))))
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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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