A359270 Number of divisors of 5*n-3 of form 5*k+3.

0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 3, 0, 0, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 0, 2, 0, 1, 1, 1, 0, 3, 0, 0, 2, 1, 0, 1, 0, 2, 1, 0, 1, 4, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 4, 0, 1, 1, 1, 0, 3, 0, 2, 1, 0, 0, 2, 1, 0, 2, 3, 0, 1, 0, 1, 1, 0, 0, 5, 1, 1, 1

Offset: 1

Author

Seiichi Manyama, Dec 23 2022

Keywords

• nonn
• easy

Comments

Also number of divisors of 5*n-3 of form 5*k+4.

Links

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

Crossrefs

Cf. A001878, A001899, A359237.

Programs

Mathematica

a[n_] := DivisorSum[5*n-3, 1 &, Mod[#, 5] == 3 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)

PARI

a(n) = sumdiv(5*n-3, d, d%5==3);

PARI

a(n) = sumdiv(5*n-3, d, d%5==4);

PARI

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

PARI

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

Formula

a(n) = A001878(5*n-3) = A001899(5*n-3).

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

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