A364031 Expansion of Sum_{k>0} k * x^k / (1 + x^(4*k)).

1, 2, 3, 4, 4, 6, 7, 8, 10, 8, 11, 12, 12, 14, 12, 16, 18, 20, 19, 16, 20, 22, 23, 24, 21, 24, 30, 28, 28, 24, 31, 32, 34, 36, 28, 40, 36, 38, 36, 32, 42, 40, 43, 44, 40, 46, 47, 48, 50, 42, 54, 48, 52, 60, 44, 56, 58, 56, 59, 48, 60, 62, 67, 64, 48, 68, 67, 72, 68, 56, 71, 80, 74, 72, 63, 76, 76, 72, 79

Offset

1,2

Links

Table of n, a(n) for n=1..79.

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(4*k-3) / (1 - x^(4*k-3))^2.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A050469, A364012, A364019.

Cf. A363037.

Sequence in context: A100476 A290083 A248517 * A007896 A351006 A325682

Adjacent sequences: A364028 A364029 A364030 * A364032 A364033 A364034

Keyword

nonn

Author

Seiichi Manyama, Jul 01 2023

Status

approved