A359237 Number of divisors of 5*n-3 of form 5*k+1.

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

Offset

1,3

Comments

Also number of divisors of 5*n-3 of form 5*k+2.

Links

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

Formula

a(n) = A001876(5*n-3) = A001877(5*n-3).

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

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

Mathematica

a[n_] := DivisorSum[5*n-3, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)

Prog

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

Crossrefs

Cf. A001876, A001877, A359233, A359236, A359238.

Sequence in context: A235726 A060938 A087942 * A327925 A320012 A359508

Adjacent sequences: A359234 A359235 A359236 * A359238 A359239 A359240

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 22 2022

Status

approved