A359189 a(n) = Sum_{d|n} d * 3^(n/d-1).

1, 5, 12, 37, 86, 276, 736, 2261, 6597, 19870, 59060, 177780, 531454, 1595816, 4783272, 14353429, 43046738, 129154113, 387420508, 1162301342, 3486786672, 10460471356, 31381059632, 94143540948, 282429536911, 847289672390, 2541865848120, 7625600676808

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Formula

G.f.: Sum_{k>=1} k * x^k/(1 - 3 * x^k).

G.f.: Sum_{k>=1} 3^(k-1) * x^k/(1 - x^k)^2.

Mathematica

a[n_] := DivisorSum[n, 3^(n/#-1)*# &]; Array[a, 28] (* Amiram Eldar, Aug 27 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, d*3^(n/d-1));
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-3*x^k)))
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, 3^(k-1)*x^k/(1-x^k)^2))

Crossrefs

Cf. A054599, A359190.

Sequence in context: A368094 A077918 A300534 * A297909 A220705 A034752

Adjacent sequences: A359186 A359187 A359188 * A359190 A359191 A359192

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 19 2022

Status

approved