A359233 Number of divisors of 5*n-1 of form 5*k+1.

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

Offset

1,5

Comments

Also number of divisors of 5*n-1 of form 5*k+4.

Links

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

Formula

a(n) = A001876(5*n-1) = A001899(5*n-1).

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A078703, A099774, A359211.

Cf. A001876, A001899, A359236, A359237, A359238.

Sequence in context: A126864 A348928 A124766 * A337323 A344770 A293895

Adjacent sequences: A359230 A359231 A359232 * A359234 A359235 A359236

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 22 2022

Status

approved