A363899 Expansion of Sum_{k>0} k * x^(3*k) / (1 - x^(5*k)).

0, 0, 1, 0, 0, 2, 0, 1, 3, 0, 0, 4, 1, 0, 5, 2, 0, 7, 0, 0, 7, 0, 1, 11, 0, 2, 9, 1, 0, 10, 0, 4, 12, 0, 0, 14, 0, 1, 16, 5, 0, 14, 1, 0, 15, 2, 0, 23, 0, 0, 17, 4, 1, 21, 0, 9, 19, 1, 0, 20, 0, 0, 22, 8, 5, 24, 0, 1, 26, 0, 0, 37, 1, 0, 25, 2, 0, 33, 0, 10, 27, 0, 1, 31, 0, 2, 29, 12, 0

Offset

1,6

Links

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

Formula

a(n) = Sum_{d|n, n/d==3 mod 5} d.

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

Mathematica

a[n_] := DivisorSum[n, # &, Mod[n/#, 5] == 3 &]; Array[a, 100] (* Amiram Eldar, Jun 27 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d%5==3)*d);

Crossrefs

Cf. A363897, A363898, A363900.

Cf. A001878, A284281.

Sequence in context: A154312 A236076 A364021 * A119900 A328376 A141097

Adjacent sequences: A363896 A363897 A363898 * A363900 A363901 A363902

Keyword

nonn

Author

Seiichi Manyama, Jun 27 2023

Status

approved