cp's OEIS Frontend

A364021 Expansion of Sum_{k>0} k * x^(3*k) / (1 + x^(5*k)).

%I A364021 #22 Jul 03 2023 00:59:26
%S A364021 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,
%T A364021 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,
%U A364021 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
%N A364021 Expansion of Sum_{k>0} k * x^(3*k) / (1 + x^(5*k)).
%H A364021 Seiichi Manyama, <a href="/A364021/b364021.txt">Table of n, a(n) for n = 1..10000</a>
%F A364021 G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-2) / (1 - x^(5*k-2))^2.
%F A364021 a(n) = -Sum_{d|n, n/d==3 (mod 5)} (-1)^(n/d) * d.
%t A364021 a[n_] := -DivisorSum[n, (-1)^(n/#) * # &, Mod[n/#, 5] == 3 &]; Array[a, 100] (* _Amiram Eldar_, Jul 03 2023 *)
%o A364021 (PARI) a(n) = -sumdiv(n, d, (n/d%5==3)*(-1)^(n/d)*d);
%Y A364021 Cf. A364019, A364020, A364022.
%Y A364021 Cf. A363899.
%K A364021 sign
%O A364021 1,6
%A A364021 _Seiichi Manyama_, Jul 01 2023