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A308696 a(n) = Sum_{d|n} d^(2*d). 6
1, 17, 730, 65553, 9765626, 2176783082, 678223072850, 281474976776209, 150094635296999851, 100000000000009765642, 81402749386839761113322, 79496847203390846310290154, 91733330193268616658399616010, 123476695691247935826908004929122 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(2*k-1))) = Sum_{k>=1} a(k)*x^k/k.
G.f.: Sum_{k>=1} k^(2*k) * x^k/(1 - x^k).
MATHEMATICA
a[n_] := DivisorSum[n, #^(2*#) &]; Array[a, 14] (* Amiram Eldar, May 09 2021 *)
PROG
(PARI) {a(n) = sumdiv(n, d, d^(2*d))}
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(2*k-1)))))
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(2*k)*x^k/(1-x^k)))
CROSSREFS
Column k=2 of A308698.
Sequence in context: A128274 A012085 A298306 * A308594 A308570 A218423
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 17 2019
STATUS
approved

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Last modified June 13 00:51 EDT 2024. Contains 373362 sequences. (Running on oeis4.)