A359227 Number of divisors of 4*n-3 of form 4*k+1.

1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 3, 4, 2, 2, 2, 2, 4, 2, 2, 4, 2, 4, 2, 2, 2, 2, 4, 2, 4, 2, 2, 4, 3, 2, 2, 2, 4, 4, 2, 2, 2, 4, 2, 2, 2, 4, 6, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 2, 4, 2, 2, 4, 3, 2, 4, 2, 4, 2, 2, 2, 2, 6, 2, 4, 2, 2, 4, 2, 2, 4

Offset

1,2

Links

Table of n, a(n) for n=1..90.

Formula

a(n) = A001826(4*n-3).

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001826, A078703.

Sequence in context: A187188 A358618 A183027 * A078178 A306396 A355035

Adjacent sequences: A359224 A359225 A359226 * A359228 A359229 A359230

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 22 2022

Status

approved