A359269 Number of divisors of 5*n-2 of form 5*k+2.

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

Offset: 1

Author

Seiichi Manyama, Dec 23 2022

Keywords

• nonn
• easy

Comments

Also number of divisors of 5*n-2 of form 5*k+4.

Links

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

Crossrefs

Cf. A001877, A001899, A359236.

Programs

Mathematica

a[n_] := DivisorSum[5*n-2, 1 &, Mod[#, 5] == 2 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)

PARI

a(n) = sumdiv(5*n-2, d, d%5==2);

PARI

a(n) = sumdiv(5*n-2, d, d%5==4);

PARI

my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1-x^(5*k-1)))))

PARI

my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(4*k-2)/(1-x^(5*k-3)))))

Formula

a(n) = A001877(5*n-2) = A001899(5*n-2).

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

G.f.: Sum_{k>0} x^(4*k-2)/(1 - x^(5*k-3)).