A363969 Expansion of Sum_{k>0} k^2 * x^(2*k-1) / (1 - x^(2*k-1)).

1, 1, 5, 1, 10, 5, 17, 1, 30, 10, 37, 5, 50, 17, 78, 1, 82, 30, 101, 10, 142, 37, 145, 5, 179, 50, 226, 17, 226, 78, 257, 1, 330, 82, 350, 30, 362, 101, 454, 10, 442, 142, 485, 37, 632, 145, 577, 5, 642, 179, 762, 50, 730, 226, 830, 17, 946, 226, 901, 78, 962, 257, 1191, 1, 1148, 330, 1157, 82

Offset

1,3

Links

Table of n, a(n) for n=1..68.

Formula

a(n) = Sum_{d|n, d==1 mod 2} ((d+1)/2)^2.

Mathematica

a[n_] := DivisorSum[n, ((# + 1)/2)^2 &, OddQ[#] &]; Array[a, 100] (* Amiram Eldar, Jun 30 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (d%2==1)*((d+1)/2)^2);

Crossrefs

Cf. A001227, A113415.

Cf. A050999, A363974.

Sequence in context: A063475 A348689 A329752 * A135855 A116547 A013612

Adjacent sequences: A363966 A363967 A363968 * A363970 A363971 A363972

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 30 2023

Status

approved