A363898 Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(5*k)).

0, 1, 0, 2, 0, 3, 1, 4, 0, 5, 0, 7, 0, 9, 0, 8, 1, 9, 0, 10, 3, 12, 0, 14, 0, 13, 1, 18, 0, 15, 0, 17, 0, 19, 5, 21, 1, 19, 0, 20, 0, 28, 0, 24, 0, 23, 1, 28, 7, 25, 3, 27, 0, 29, 0, 36, 1, 29, 0, 35, 0, 32, 9, 34, 0, 36, 1, 38, 0, 45, 0, 43, 0, 39, 0, 38, 12, 39, 0, 40, 3, 42, 0, 63, 5, 43, 1

Offset

1,4

Links

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

Formula

a(n) = Sum_{d|n, n/d==2 mod 5} d.

G.f.: Sum_{k>0} x^(5*k-3) / (1 - x^(5*k-3))^2.

Mathematica

a[n_] := DivisorSum[n, # &, Mod[n/#, 5] == 2 &]; Array[a, 100] (* Amiram Eldar, Jun 27 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d%5==2)*d);

Crossrefs

Cf. A363897, A363899, A363900.

Cf. A001877, A284280.

Sequence in context: A279119 A249738 A364020 * A110514 A338503 A249122

Adjacent sequences: A363895 A363896 A363897 * A363899 A363900 A363901

Keyword

nonn

Author

Seiichi Manyama, Jun 27 2023

Status

approved