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A364012
Expansion of Sum_{k>0} k * x^k / (1 + x^(3*k)).
6
1, 2, 3, 3, 5, 6, 8, 6, 9, 9, 11, 9, 14, 16, 15, 11, 17, 18, 20, 13, 24, 21, 23, 18, 26, 28, 27, 24, 29, 27, 32, 22, 33, 33, 40, 27, 38, 40, 42, 25, 41, 48, 44, 31, 45, 45, 47, 33, 57, 47, 51, 42, 53, 54, 56, 48, 60, 57, 59, 39, 62, 64, 72, 43, 70, 63, 68, 49, 69, 72, 71, 54, 74, 76, 78
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k>0} (-1)^(k-1) * x^(3*k-2) / (1 - x^(3*k-2))^2.
a(n) = -Sum_{d|n, n/d==1 (mod 3)} (-1)^(n/d) * d.
MATHEMATICA
a[n_] := -DivisorSum[n, (-1)^(n/#) * # &, Mod[n/#, 3] == 1 &]; Array[a, 100] (* Amiram Eldar, Jul 01 2023 *)
PROG
(PARI) a(n) = -sumdiv(n, d, (n/d%3==1)*(-1)^(n/d)*d);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 01 2023
STATUS
approved