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A364104 Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k-1)).

%I A364104 #18 Jul 12 2023 01:01:12
%S A364104 1,2,3,4,6,6,7,8,10,10,13,12,14,14,15,16,21,18,19,22,22,22,27,24,26,
%T A364104 26,27,28,37,30,34,32,34,34,41,36,38,40,39,40,49,46,43,44,49,46,57,48,
%U A364104 50,50,51,52,68,54,55,58,58,58,72,60,66,62,63,70,79,66,67,68,70,70,83,72,77,76,82,76,96
%N A364104 Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k-1)).
%H A364104 Seiichi Manyama, <a href="/A364104/b364104.txt">Table of n, a(n) for n = 1..10000</a>
%F A364104 a(n) = (1/5) * Sum_{d | 5*n-1, d==4 (mod 5)} (d+1).
%F A364104 G.f.: Sum_{k>0} x^(4*k-3) / (1 - x^(5*k-4))^2.
%t A364104 a[n_] := DivisorSum[5*n - 1, # + 1 &, Mod[#, 5] == 4 &]/5; Array[a, 100] (* _Amiram Eldar_, Jul 12 2023 *)
%o A364104 (PARI) a(n) = sumdiv(5*n-1, d, (d%5==4)*(d+1))/5;
%Y A364104 Cf. A364105, A364106, A364107.
%Y A364104 Cf. A363028, A363155, A364096.
%Y A364104 Cf. A359233, A364100.
%K A364104 nonn
%O A364104 1,2
%A A364104 _Seiichi Manyama_, Jul 05 2023