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A364021
Expansion of Sum_{k>0} k * x^(3*k) / (1 + x^(5*k)).
5
0, 0, 1, 0, 0, 2, 0, -1, 3, 0, 0, 4, 1, 0, 5, -2, 0, 5, 0, 0, 7, 0, 1, 5, 0, 2, 9, -1, 0, 10, 0, -4, 12, 0, 0, 10, 0, -1, 16, -5, 0, 14, 1, 0, 15, 2, 0, 9, 0, 0, 17, 4, 1, 15, 0, -9, 19, -1, 0, 20, 0, 0, 22, -8, 5, 24, 0, -1, 26, 0, 0, 11, 1, 0, 25, -2, 0, 31, 0, -10, 27, 0, 1, 25, 0, 2, 29, -12, 0, 25
OFFSET
1,6
LINKS
FORMULA
G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-2) / (1 - x^(5*k-2))^2.
a(n) = -Sum_{d|n, n/d==3 (mod 5)} (-1)^(n/d) * d.
MATHEMATICA
a[n_] := -DivisorSum[n, (-1)^(n/#) * # &, Mod[n/#, 5] == 3 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)
PROG
(PARI) a(n) = -sumdiv(n, d, (n/d%5==3)*(-1)^(n/d)*d);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 01 2023
STATUS
approved