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A359239
Number of divisors of 3*n-2 of form 3*k+2.
7
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
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
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 22 2022
STATUS
approved