A359240 Number of divisors of 4*n-3 of form 4*k+3.

0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 4, 0, 0, 2, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, 0, 3, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 4, 0, 0, 4, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 4, 0, 0, 4

Offset

1,6

Links

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

Formula

a(n) = A001842(4*n-3).

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

Mathematica

a[n_] := DivisorSum[4*n-3, 1 &, Mod[#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)

Prog

(PARI) a(n) = sumdiv(4*n-3, d, d%4==3);
(PARI) my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/(1-x^(4*k-1)))))

Crossrefs

Cf. A359239, A359241.

Cf. A001842.

Sequence in context: A096142 A216921 A344982 * A280285 A033719 A171608

Adjacent sequences: A359237 A359238 A359239 * A359241 A359242 A359243

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 22 2022

Status

approved