A363972 Expansion of Sum_{k>0} k^2 * x^(4*k-3) / (1 - x^(4*k-3)).

1, 1, 1, 1, 5, 1, 1, 1, 10, 5, 1, 1, 17, 1, 5, 1, 26, 10, 1, 5, 37, 1, 1, 1, 54, 17, 10, 1, 65, 5, 1, 1, 82, 26, 5, 10, 101, 1, 17, 5, 122, 37, 1, 1, 158, 1, 1, 1, 170, 54, 26, 17, 197, 10, 5, 1, 226, 65, 1, 5, 257, 1, 46, 1, 310, 82, 1, 26, 325, 5, 1, 10, 362, 101, 54, 1, 401, 17, 1, 5, 451, 122, 1

Offset

1,5

Links

Table of n, a(n) for n=1..83.

Formula

a(n) = Sum_{d|n, d==1 mod 4} ((d+3)/4)^2.

Mathematica

a[n_] := DivisorSum[n, ((#+3)/4)^2 &, Mod[#, 4] == 1 &]; Array[a, 100] (* Amiram Eldar, Jun 30 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (d%4==1)*((d+3)/4)^2);

Crossrefs

Cf. A001826, A363903.

Cf. A050450, A363977.

Sequence in context: A360720 A010130 A361063 * A206773 A229526 A204007

Adjacent sequences: A363969 A363970 A363971 * A363973 A363974 A363975

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 30 2023

Status

approved