A359233 Number of divisors of 5*n-1 of form 5*k+1.

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

Offset: 1

Author

Seiichi Manyama, Dec 22 2022

Keywords

• nonn
• easy

Comments

Also number of divisors of 5*n-1 of form 5*k+4.

Links

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

Crossrefs

Cf. A078703, A099774, A359211.

Cf. A001876, A001899, A359236, A359237, A359238.

Programs

Mathematica

a[n_] := DivisorSum[5*n-1, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)

PARI

a(n) = sumdiv(5*n-1, d, d%5==1);

PARI

a(n) = sumdiv(5*n-1, d, d%5==4);

PARI

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

PARI

my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(4*k-3)/(1-x^(5*k-4))))

Formula

a(n) = A001876(5*n-1) = A001899(5*n-1).

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

G.f.: Sum_{k>0} x^(4*k-3)/(1 - x^(5*k-4)).