A359325 Number of divisors of 6*n-3 of form 6*k+5.

0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 0, 0, 2, 0, 1, 1, 0, 1, 2, 0, 0, 1, 2, 1, 1, 0, 0, 2, 0, 1, 1, 0, 2, 1, 0, 0, 1, 2, 0, 2, 1, 1, 2, 0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 2, 1, 0, 0, 1, 2, 1, 1

Offset

1,18

Links

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

Formula

a(n) = A319995(6*n-3).

G.f.: Sum_{k>0} x^(3*k)/(1 - x^(6*k-1)).

G.f.: Sum_{k>0} x^(5*k-2)/(1 - x^(6*k-3)).

Mathematica

a[n_] := DivisorSum[6*n-3, 1 &, Mod[#, 6] == 5 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)

Prog

(PARI) a(n) = sumdiv(6*n-3, d, d%6==5);
(PARI) my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/(1-x^(6*k-1)))))
(PARI) my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(5*k-2)/(1-x^(6*k-3)))))

Crossrefs

Cf. A319995, A359305, A359324, A359326, A359327.

Sequence in context: A220945 A089224 A344987 * A325122 A234578 A069859

Adjacent sequences: A359322 A359323 A359324 * A359326 A359327 A359328

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 25 2022

Status

approved