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

1,13

Links

Table of n, a(n) for n=1..104.

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).

Mathematica

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

Prog

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

Crossrefs

Cf. A002654, A363037, A364011, A364043.

Cf. A279060.

Sequence in context: A178686 A142724 A174656 * A373335 A178798 A318277

Adjacent sequences: A364044 A364045 A364046 * A364048 A364049 A364050

Keyword

nonn

Author

Seiichi Manyama, Jul 03 2023

Status

approved