A363859 Number of divisors of 7*n-1 of the form 7*k+2.

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

Offset: 1

Author

Seiichi Manyama, Jun 24 2023

Keywords

• nonn
• changed

Comments

Also number of divisors of 7*n-1 of form 7*k+3.

Crossrefs

Cf. A363795, A363805.

Programs

Mathematica

a[n_] := DivisorSum[7*n - 1, 1 &, Mod[#, 7] == 2 &]; Array[a, 100] (* Amiram Eldar, Jun 25 2023 *)

PARI

a(n) = sumdiv(7*n-1, d, d%7==2);

Formula

a(n) = A363795(7*n-1) = A363805(7*n-1).

G.f.: Sum_{k>0} x^(3*k-2)/(1 - x^(7*k-5)).

G.f.: Sum_{k>0} x^(2*k-1)/(1 - x^(7*k-4)).

a(n) = Sum_{d|(7n-1)} c((d-2)/7), where c(n) = 1-ceiling(n)+floor(n). - Wesley Ivan Hurt, Sep 05 2025