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A308692
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a(n) = Sum_{d|n} d^(2*(n/d - 1)).
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5
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1, 2, 2, 6, 2, 27, 2, 82, 83, 283, 2, 2047, 2, 4147, 7188, 20546, 2, 125964, 2, 343407, 533844, 1048699, 2, 10076747, 390627, 16777387, 43053284, 84003927, 2, 667311413, 2, 1342439682, 3486799044, 4294967587, 249905428, 52916914768, 2, 68719477099, 282429565044
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OFFSET
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1,2
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..3143
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FORMULA
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L.g.f.: -log(Product_{k>=1} (1 - k^2*x^k)^(1/k^3)) = Sum_{k>=1} a(k)*x^k/k.
a(p) = 2 for prime p.
G.f.: Sum_{k>=1} x^k/(1 - k^2*x^k). - Ilya Gutkovskiy, Jul 25 2019
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MAPLE
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N:=100: # for a(1)..a(N)
g:= add(x^k/(1-k^2*x^k), k=1..N):
S:= series(g, x, N+1):
seq(coeff(S, x, j), j=1..N); # Robert Israel, Apr 05 2020
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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^3)))))
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CROSSREFS
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Column k=2 of A308694.
Sequence in context: A286376 A100346 A306387 * A319352 A300834 A293214
Adjacent sequences: A308689 A308690 A308691 * A308693 A308694 A308695
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KEYWORD
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nonn,look
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AUTHOR
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Seiichi Manyama, Jun 17 2019
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STATUS
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approved
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