A359186 a(n) = Sum_{d|n} d * 4^(d-1).

1, 9, 49, 265, 1281, 6201, 28673, 131337, 589873, 2622729, 11534337, 50338105, 218103809, 939552777, 4026533169, 17180000521, 73014444033, 309238241337, 1305670057985, 5497560761865, 23089744212017, 96757034778633, 404620279021569, 1688849910733113

Offset: 1

Author

Seiichi Manyama, Dec 19 2022

Keywords

• nonn
• easy

Crossrefs

Cf. A002129, A083413, A359018.

Cf. A167531, A339684, A359190.

Programs

Mathematica

a[n_] := DivisorSum[n, 4^(#-1)*# &]; Array[a, 24] (* Amiram Eldar, Aug 27 2023 *)

PARI

a(n) = sumdiv(n, d, d*4^(d-1));

PARI

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

Formula

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