A364046 Expansion of Sum_{k>0} x^(4*k) / (1 + x^(5*k)).

0, 0, 0, 1, 0, 0, 0, 1, -1, 0, 0, 1, 0, 1, 0, 1, 0, -1, -1, 1, 0, 0, 0, 2, 0, 0, -1, 2, -1, 0, 0, 1, 0, 1, 0, 0, 0, -1, -1, 1, 0, 1, 0, 2, -1, 0, 0, 2, -1, 0, 0, 1, 0, 0, 0, 2, -1, -1, -1, 1, 0, 0, -1, 2, 0, 0, 0, 2, -1, 1, 0, 1, 0, 1, 0, 0, 0, -1, -1, 1, -1, 0, 0, 3, 0, 0, -1, 2, -1, -1, 0, 1, 0, 1, -1, 2, 0, 0, -2

Offset

1,24

Links

Table of n, a(n) for n=1..99.

Formula

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

a(n) = Sum_{d|n, d==4 (mod 5)} (-1)^d.

Mathematica

a[n_] := DivisorSum[n, (-1)^# &, Mod[#, 5] == 4 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (d%5==4)*(-1)^d);

Crossrefs

Cf. A364043, A364044, A364045.

Cf. A001899, A364022.

Sequence in context: A105964 A303051 A324044 * A001899 A059882 A303206

Adjacent sequences: A364043 A364044 A364045 * A364047 A364048 A364049

Keyword

sign

Author

Seiichi Manyama, Jul 03 2023

Status

approved