A359236 Number of divisors of 5*n-2 of form 5*k+1.

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

Offset

1,4

Comments

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

Links

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

Formula

a(n) = A001876(5*n-2) = A001878(5*n-2).

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

G.f.: Sum_{k>0} x^(3*k-2)/(1 - x^(5*k-4)).

Mathematica

a[n_] := DivisorSum[5*n-2, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)

Prog

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

Crossrefs

Cf. A001876, A001878, A359233, A359237, A359238.

Sequence in context: A280509 A153096 A343407 * A320010 A210763 A281681

Adjacent sequences: A359233 A359234 A359235 * A359237 A359238 A359239

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 22 2022

Status

approved