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A364045
Expansion of Sum_{k>0} x^(3*k) / (1 + x^(5*k)).
3
0, 0, 1, 0, 0, 1, 0, -1, 1, 0, 0, 1, 1, 0, 1, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, -1, 0, 1, 0, -1, 2, 0, 0, 0, 0, -1, 2, -1, 0, 1, 1, 0, 1, 1, 0, -1, 0, 0, 1, 1, 1, 0, 0, -2, 1, -1, 0, 1, 0, 0, 2, -1, 1, 2, 0, -1, 2, 0, 0, -1, 1, 0, 1, -1, 0, 1, 0, -1, 1, 0, 1, 0, 0, 1, 1, -2, 0, 0, 1, 1, 2, 0, 0, -1, 0, -1, 2, 0, 0, 1
OFFSET
1,33
FORMULA
G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-2) / (1 - x^(5*k-2)).
a(n) = -Sum_{d|n, d==3 (mod 5)} (-1)^d.
MATHEMATICA
a[n_] := -DivisorSum[n, (-1)^# &, Mod[#, 5] == 3 &]; Array[a, 100] (* Amiram Eldar, Jul 05 2023 *)
PROG
(PARI) a(n) = -sumdiv(n, d, (d%5==3)*(-1)^d);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 03 2023
STATUS
approved