A359289 Number of divisors of 4*n-2 of form 4*k+1.

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

Offset

1,3

Links

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

Formula

a(n) = A001826(4*n-2).

G.f.: Sum_{k>0} x^k/(1 - x^(4*k-2)).

G.f.: Sum_{k>0} x^(2*k-1)/(1 - x^(4*k-3)).

Mathematica

a[n_] := DivisorSum[4*n-2, 1 &, Mod[#, 4] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)

Prog

(PARI) a(n) = sumdiv(4*n-2, d, d%4==1);
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(4*k-2))))
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(2*k-1)/(1-x^(4*k-3))))

Crossrefs

Cf. A001826, A078703, A359227.

Sequence in context: A290085 A322867 A163109 * A286574 A329320 A316112

Adjacent sequences: A359286 A359287 A359288 * A359290 A359291 A359292

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 24 2022

Status

approved