A308696 a(n) = Sum_{d|n} d^(2*d).

1, 17, 730, 65553, 9765626, 2176783082, 678223072850, 281474976776209, 150094635296999851, 100000000000009765642, 81402749386839761113322, 79496847203390846310290154, 91733330193268616658399616010, 123476695691247935826908004929122

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..214

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.

Cf. A073705, A308753, A308756.

Sequence in context: A128274 A012085 A298306 * A308594 A308570 A218423

Adjacent sequences: A308693 A308694 A308695 * A308697 A308698 A308699

Keyword

nonn

Author

Seiichi Manyama, Jun 17 2019

Status

approved