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A364096 Expansion of Sum_{k>0} k * x^(4*k-3) / (1 - x^(5*k-4)).

%I A364096 #17 Jul 12 2023 01:01:01
%S A364096 1,1,1,1,3,1,1,1,4,1,3,1,5,1,1,1,8,1,1,4,7,1,3,1,8,1,1,1,15,1,4,1,10,
%T A364096 1,3,1,11,6,1,1,14,4,1,1,17,1,9,1,14,1,1,1,20,1,1,8,16,1,8,1,21,1,1,4,
%U A364096 28,1,1,1,19,1,3,1,26,10,4,1,27,1,1,6,22,1,13,1,23,4,8,1,26,1,1,12,29,1,3,1
%N A364096 Expansion of Sum_{k>0} k * x^(4*k-3) / (1 - x^(5*k-4)).
%H A364096 Seiichi Manyama, <a href="/A364096/b364096.txt">Table of n, a(n) for n = 1..10000</a>
%F A364096 a(n) = (1/5) * Sum_{d | 5*n-1, d==1 (mod 5)} (d+4).
%F A364096 G.f.: Sum_{k>0} x^k / (1 - x^(5*k-1))^2.
%t A364096 a[n_] := DivisorSum[5*n - 1, # + 4 &, Mod[#, 5] == 1 &]/5; Array[a, 100] (* _Amiram Eldar_, Jul 12 2023 *)
%o A364096 (PARI) a(n) = sumdiv(5*n-1, d, (d%5==1)*(d+4))/5;
%Y A364096 Cf. A359233, A364092.
%Y A364096 Cf. A363028, A363155, A364104.
%K A364096 nonn
%O A364096 1,5
%A A364096 _Seiichi Manyama_, Jul 04 2023