A359307 Number of divisors of 6*n-3 of form 6*k+1.

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

Offset: 1

Author

Seiichi Manyama, Dec 25 2022

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A279060, A359305, A359306, A359308, A359309.

Programs

Mathematica

a[n_] := DivisorSum[6*n-3, 1 &, Mod[#, 6] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)

PARI

a(n) = sumdiv(6*n-3, d, d%6==1);

PARI

my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(6*k-3))))

PARI

my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(3*k-2)/(1-x^(6*k-5))))

Formula

a(n) = A279060(6*n-3).

G.f.: Sum_{k>0} x^k/(1 - x^(6*k-3)).

G.f.: Sum_{k>0} x^(3*k-2)/(1 - x^(6*k-5)).