A364019 Expansion of Sum_{k>0} k * x^k / (1 + x^(5*k)).

1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 12, 10, 13, 14, 15, 15, 17, 15, 19, 20, 22, 24, 23, 20, 25, 25, 27, 28, 29, 25, 32, 30, 36, 34, 35, 29, 37, 38, 39, 40, 42, 37, 43, 48, 45, 45, 47, 37, 49, 50, 52, 50, 53, 45, 60, 55, 57, 58, 59, 50, 62, 64, 66, 60, 65, 60, 67, 68, 69, 70, 72, 58, 73, 74, 75, 75, 84, 62, 79, 75

Offset

1,2

Links

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

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-4) / (1 - x^(5*k-4))^2.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A364020, A364021, A364022.

Cf. A363897.

Sequence in context: A357005 A267508 A163382 * A343127 A094017 A092762

Adjacent sequences: A364016 A364017 A364018 * A364020 A364021 A364022

Keyword

nonn

Author

Seiichi Manyama, Jul 01 2023

Status

approved