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A364046
Expansion of Sum_{k>0} x^(4*k) / (1 + x^(5*k)).
3
0, 0, 0, 1, 0, 0, 0, 1, -1, 0, 0, 1, 0, 1, 0, 1, 0, -1, -1, 1, 0, 0, 0, 2, 0, 0, -1, 2, -1, 0, 0, 1, 0, 1, 0, 0, 0, -1, -1, 1, 0, 1, 0, 2, -1, 0, 0, 2, -1, 0, 0, 1, 0, 0, 0, 2, -1, -1, -1, 1, 0, 0, -1, 2, 0, 0, 0, 2, -1, 1, 0, 1, 0, 1, 0, 0, 0, -1, -1, 1, -1, 0, 0, 3, 0, 0, -1, 2, -1, -1, 0, 1, 0, 1, -1, 2, 0, 0, -2
OFFSET
1,24
FORMULA
G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-1) / (1 - x^(5*k-1)).
a(n) = Sum_{d|n, d==4 (mod 5)} (-1)^d.
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^# &, Mod[#, 5] == 4 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d%5==4)*(-1)^d);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 03 2023
STATUS
approved