A364011 Expansion of Sum_{k>0} x^k / (1 + x^(3*k)).

1, 1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 0, 2, 2, 1, -1, 1, 1, 2, -1, 2, 0, 1, 0, 2, 2, 1, 0, 1, 0, 2, -1, 1, 0, 2, 0, 2, 2, 2, -2, 1, 2, 2, -1, 1, 0, 1, -1, 3, 1, 1, 0, 1, 1, 2, 0, 2, 0, 1, -1, 2, 2, 2, -2, 2, 0, 2, -1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, -3, 1, 0, 1, 0, 2, 2, 1, -2, 1, 0, 4, -1, 2, 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. A364012, A364013.

Cf. A002654, A363037.

Programs

Mathematica

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

PARI

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

Formula

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

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