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A364022 Expansion of Sum_{k>0} k * x^(4*k) / (1 + x^(5*k)).

%I A364022 #22 Jul 03 2023 00:59:04
%S A364022 0,0,0,1,0,0,0,2,-1,0,0,3,0,1,0,4,0,-2,-1,5,0,0,0,7,0,0,-3,9,-1,0,0,8,
%T A364022 0,1,0,5,0,-2,-1,10,0,3,0,12,-5,0,0,14,-1,0,0,13,0,-5,0,18,-3,-2,-1,
%U A364022 15,0,0,-7,17,0,0,0,19,-1,5,0,13,0,1,0,15,0,-2,-1,20,-9,0,0,28,0,0,-3,24,-1,-10,0
%N A364022 Expansion of Sum_{k>0} k * x^(4*k) / (1 + x^(5*k)).
%H A364022 Seiichi Manyama, <a href="/A364022/b364022.txt">Table of n, a(n) for n = 1..10000</a>
%F A364022 G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-1) / (1 - x^(5*k-1))^2.
%F A364022 a(n) = Sum_{d|n, n/d==4 (mod 5)} (-1)^(n/d) * d.
%t A364022 a[n_] := DivisorSum[n, (-1)^(n/#) * # &, Mod[n/#, 5] == 4 &]; Array[a, 100] (* _Amiram Eldar_, Jul 03 2023 *)
%o A364022 (PARI) a(n) = sumdiv(n, d, (n/d%5==4)*(-1)^(n/d)*d);
%Y A364022 Cf. A364019, A364020, A364021.
%Y A364022 Cf. A363900.
%K A364022 sign
%O A364022 1,8
%A A364022 _Seiichi Manyama_, Jul 01 2023