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A308688
a(n) = Sum_{d|n} d^(2*n/d - 1).
4
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
OFFSET
1,2
LINKS
FORMULA
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.
G.f.: Sum_{k>=1} k*x^k/(1 - k^2*x^k). - Ilya Gutkovskiy, Jul 25 2019
MATHEMATICA
a[n_] := DivisorSum[n, #^(2*n/# - 1) &]; Array[a, 37] (* Amiram Eldar, May 09 2021 *)
PROG
(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)))))
CROSSREFS
Column k=2 of A308690.
Sequence in context: A324159 A220847 A127611 * A324501 A359112 A342675
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 17 2019
STATUS
approved