A359244 Number of divisors of 5*n-4 of form 5*k+2.

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

Offset

1,8

Comments

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

Links

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

Formula

a(n) = A001877(5*n-4) = A001878(5*n-4).

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

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

Mathematica

a[n_] := DivisorSum[5*n-4, 1 &, Mod[#, 5] == 2 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)

Prog

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

Crossrefs

Cf. A001877, A001878.

Sequence in context: A214269 A130027 A116949 * A204427 A178146 A305435

Adjacent sequences: A359241 A359242 A359243 * A359245 A359246 A359247

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 22 2022

Status

approved