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A364019 Expansion of Sum_{k>0} k * x^k / (1 + x^(5*k)).

%I A364019 #23 Jul 03 2023 00:59:35
%S A364019 1,2,3,4,5,5,7,8,9,10,12,10,13,14,15,15,17,15,19,20,22,24,23,20,25,25,
%T A364019 27,28,29,25,32,30,36,34,35,29,37,38,39,40,42,37,43,48,45,45,47,37,49,
%U A364019 50,52,50,53,45,60,55,57,58,59,50,62,64,66,60,65,60,67,68,69,70,72,58,73,74,75,75,84,62,79,75
%N A364019 Expansion of Sum_{k>0} k * x^k / (1 + x^(5*k)).
%H A364019 Seiichi Manyama, <a href="/A364019/b364019.txt">Table of n, a(n) for n = 1..10000</a>
%F A364019 G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-4) / (1 - x^(5*k-4))^2.
%F A364019 a(n) = -Sum_{d|n, n/d==1 (mod 5)} (-1)^(n/d) * d.
%t A364019 a[n_] := -DivisorSum[n, (-1)^(n/#) * # &, Mod[n/#, 5] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jul 03 2023 *)
%o A364019 (PARI) a(n) = -sumdiv(n, d, (n/d%5==1)*(-1)^(n/d)*d);
%Y A364019 Cf. A364020, A364021, A364022.
%Y A364019 Cf. A363897.
%K A364019 nonn
%O A364019 1,2
%A A364019 _Seiichi Manyama_, Jul 01 2023