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A294567
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a(n) = Sum_{d|n} d^(1 + 2*n/d).
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2
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1, 9, 28, 97, 126, 588, 344, 2049, 2917, 6174, 1332, 53764, 2198, 52320, 258648, 430081, 4914, 2463429, 6860, 8352582, 15181712, 8560308, 12168, 242240964, 48843751, 134606598, 1167064120, 1651526120, 24390, 14202123408, 29792, 25905102849, 94162701936
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OFFSET
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1,2
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COMMENTS
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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)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Mar 12 2018
G.f.: Sum_{k>0} k^3 * x^k / (1 - k^2 * x^k). - Seiichi Manyama, Jan 14 2023
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MAPLE
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f:= n -> add(d^(1+2*n/d), d=numtheory:-divisors(n)):
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MATHEMATICA
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sd[n_] := Module[{d = Divisors[n]}, Total[d^(1 + (2 n)/d)]]; Array[sd, 40] (* Harvey P. Dale, Mar 17 2020 *)
a[n_] := DivisorSum[n, #^(1 + 2*n/#) &]; Array[a, 33] (* Amiram Eldar, Oct 04 2023 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, d^(1+2*n/d)); \\ Michel Marcus, Nov 02 2017
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k^3*x^k/(1-k^2*x^k))) \\ Seiichi Manyama, Jan 14 2023
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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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