A359190 a(n) = Sum_{d|n} d * 4^(n/d-1).

1, 6, 19, 76, 261, 1074, 4103, 16536, 65593, 262686, 1048587, 4196644, 16777229, 67117098, 268436319, 1073774896, 4294967313, 17180003478, 68719476755, 274878432636, 1099511640197, 4398048608322, 17592186044439, 70368752620104, 281474976711961, 1125899940397134

Offset

1,2

Links

Table of n, a(n) for n=1..26.

Formula

G.f.: Sum_{k>=1} k * x^k/(1 - 4 * x^k).

G.f.: Sum_{k>=1} 4^(k-1) * x^k/(1 - x^k)^2.

Mathematica

a[n_] := DivisorSum[n, 4^(n/#-1)*# &]; Array[a, 26] (* Amiram Eldar, Aug 27 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, d*4^(n/d-1));
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-4*x^k)))
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, 4^(k-1)*x^k/(1-x^k)^2))

Crossrefs

Cf. A054599, A359189.

Sequence in context: A123950 A100191 A191585 * A220795 A026545 A041937

Adjacent sequences: A359187 A359188 A359189 * A359191 A359192 A359193

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 19 2022

Status

approved