A359732 a(n) = Sum_{d|n} d^(2*d-1).

1, 9, 244, 16393, 1953126, 362797308, 96889010408, 35184372105225, 16677181699666813, 10000000000001953134, 7400249944258160101212, 6624737266949237373933820, 7056410014866816666030739694, 8819763977946281130541873428720

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Formula

G.f.: Sum_{k>0} k^(2*k-1) * x^k / (1 - x^k).

Mathematica

a[n_] := DivisorSum[n, #^(2*# - 1) &]; Array[a, 15] (* Amiram Eldar, Aug 14 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(2*d-1));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(2*k-1)*x^k/(1-x^k)))

Crossrefs

Cf. A308688, A308696, A359731.

Sequence in context: A368769 A329305 A183235 * A259673 A272234 A272240

Adjacent sequences: A359729 A359730 A359731 * A359733 A359734 A359735

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 12 2023

Status

approved