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Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k-1)).
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%I #18 Jul 12 2023 01:01:12

%S 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 26,27,28,37,30,34,32,34,34,41,36,38,40,39,40,49,46,43,44,49,46,57,48,

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

%H Seiichi Manyama, <a href="/A364104/b364104.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (1/5) * Sum_{d | 5*n-1, d==4 (mod 5)} (d+1).

%F G.f.: Sum_{k>0} x^(4*k-3) / (1 - x^(5*k-4))^2.

%t a[n_] := DivisorSum[5*n - 1, # + 1 &, Mod[#, 5] == 4 &]/5; Array[a, 100] (* _Amiram Eldar_, Jul 12 2023 *)

%o (PARI) a(n) = sumdiv(5*n-1, d, (d%5==4)*(d+1))/5;

%Y Cf. A364105, A364106, A364107.

%Y Cf. A363028, A363155, A364096.

%Y Cf. A359233, A364100.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jul 05 2023