A364015 Expansion of Sum_{k>0} k * x^(2*k) / (1 + x^(3*k)).

0, 1, 0, 2, -1, 3, 0, 5, 0, 3, -1, 6, 0, 8, -3, 10, -1, 9, 0, 7, 0, 9, -1, 15, -5, 14, 0, 16, -1, 9, 0, 21, -3, 15, -8, 18, 0, 20, 0, 19, -1, 24, 0, 19, -9, 21, -1, 30, 0, 16, -3, 28, -1, 27, -16, 40, 0, 27, -1, 21, 0, 32, 0, 42, -14, 27, 0, 31, -3, 24, -1, 45, 0, 38, -15, 40, -8, 42, 0

Offset: 1

Author

Seiichi Manyama, Jul 01 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A364014, A364016.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^(n/#) * # &, Mod[n/#, 3] == 2 &]; Array[a, 100] (* Amiram Eldar, Jul 01 2023 *)

PARI

a(n) = sumdiv(n, d, (n/d%3==2)*(-1)^(n/d)*d);

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(3*k-1) / (1 - x^(3*k-1))^2.

a(n) = Sum_{d|n, n/d==2 (mod 3)} (-1)^(n/d) * d.