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A364066
Expansion of Sum_{k>0} k * x^k / (1 - x^(3*k-1)).
4
1, 2, 4, 4, 6, 6, 10, 8, 10, 10, 15, 14, 14, 14, 20, 16, 20, 18, 28, 20, 22, 24, 30, 24, 26, 30, 40, 28, 30, 30, 40, 34, 39, 34, 48, 36, 44, 38, 50, 46, 42, 44, 58, 44, 46, 46, 74, 52, 50, 50, 68, 54, 54, 62, 70, 56, 66, 58, 82, 60, 76, 64, 80, 64, 66, 66, 97, 78, 70, 74, 90, 74, 74, 80, 114, 76, 88, 78, 100
OFFSET
1,2
LINKS
FORMULA
a(n) = (1/3) * Sum_{d | 3*n-1, d==2 (mod 3)} (d+1).
G.f.: Sum_{k>0} x^(2*k-1) / (1 - x^(3*k-2))^2.
MATHEMATICA
a[n_] := DivisorSum[3*n - 1, # + 1 &, Mod[#, 3] == 2 &]/3; Array[a, 100] (* Amiram Eldar, Jul 05 2023 *)
PROG
(PARI) a(n) = sumdiv(3*n-1, d, (d%3==2)*(d+1))/3;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 04 2023
STATUS
approved