A364047 Expansion of Sum_{k>0} x^k / (1 + x^(6*k)).

1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 2, 2, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 0, 2, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 2, 0, 0, 1, 2, 1, 0, 1, 1, 0, 1, 1, 2, 2, 2, 0, 0, 2, 0, 1, 1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 1, 1, 2, 1, 1, 0, 2

Offset: 1

Author

Seiichi Manyama, Jul 03 2023

Keywords

• nonn

Crossrefs

Cf. A002654, A363037, A364011, A364043.

Cf. A279060.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^((#-1)/6) &, Mod[#, 6] == 1 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)

PARI

a(n) = sumdiv(n, d, (d%6==1)*(-1)^((d-1)/6));

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(6*k-5) / (1 - x^(6*k-5)).

a(n) = Sum_{d|n, d==1 (mod 6)} (-1)^((d-1)/6).