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

1,15

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

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)).

Mathematica

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

Prog

(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)))))

Crossrefs

Cf. A001878, A001899, A359237.

Sequence in context: A353323 A239446 A036857 * A318508 A100655 A262262

Adjacent sequences: A359267 A359268 A359269 * A359271 A359272 A359273

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 23 2022

Status

approved