A326399 Expansion of Sum_{k>=1} k * x^k / (1 - x^(3*k)).

1, 2, 3, 5, 5, 6, 8, 10, 9, 11, 11, 15, 14, 16, 15, 21, 17, 18, 20, 27, 24, 23, 23, 30, 26, 28, 27, 40, 29, 33, 32, 42, 33, 35, 40, 45, 38, 40, 42, 55, 41, 48, 44, 57, 45, 47, 47, 63, 57, 57, 51, 70, 53, 54, 56, 80, 60, 59, 59, 81, 62, 64, 72, 85, 70, 69, 68, 87, 69, 88

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{d|n, n/d==1 (mod 3)} d.

G.f.: Sum_{k>0} x^(3*k-2) / (1 - x^(3*k-2))^2. - Seiichi Manyama, Jun 29 2023

Mathematica

nmax = 70; CoefficientList[Series[Sum[k x^k/(1 - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, # &, MemberQ[{1}, Mod[n/#, 3]] &], {n, 1, 70}]

Crossrefs

Cf. A001817, A002131, A016777, A050460, A078181, A078708, A326400, A326401.

Sequence in context: A214881 A364085 A163831 * A192419 A081836 A263721

Adjacent sequences: A326396 A326397 A326398 * A326400 A326401 A326402

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 11 2019

Status

approved