A359239 Number of divisors of 3*n-2 of form 3*k+2.

0, 1, 0, 2, 0, 2, 0, 2, 1, 2, 0, 2, 0, 4, 0, 2, 0, 2, 2, 2, 0, 3, 0, 4, 0, 2, 0, 2, 2, 4, 0, 2, 0, 4, 0, 2, 0, 4, 2, 2, 1, 2, 0, 4, 0, 4, 0, 2, 2, 2, 0, 4, 0, 6, 0, 2, 0, 2, 2, 2, 0, 4, 2, 4, 0, 3, 0, 2, 2, 4, 0, 2, 0, 6, 0, 2, 0, 4, 2, 4, 0, 2, 0, 4, 2, 4, 0, 2, 2, 2

Offset

1,4

Links

Table of n, a(n) for n=1..90.

Formula

a(n) = A001822(3*n-2).

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

Mathematica

Table[Count[Divisors[3 n-2], _?(IntegerQ[(#-2)/3]&)], {n, 100}] (* Harvey P. Dale, Apr 23 2023 *)
a[n_] := DivisorSum[3*n-2, 1 &, Mod[#, 3] == 2 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)

Prog

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

Crossrefs

Cf. A001822, A359211, A359212.

Cf. A359240, A359241.

Sequence in context: A227957 A305575 A247977 * A143232 A329981 A096030

Adjacent sequences: A359236 A359237 A359238 * A359240 A359241 A359242

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 22 2022

Status

approved