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Expansion of Sum_{k>0} k * x^(4*k) / (1 - x^(5*k)).
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%I #18 Jun 29 2023 11:22:43

%S 0,0,0,1,0,0,0,2,1,0,0,3,0,1,0,4,0,2,1,5,0,0,0,7,0,0,3,9,1,0,0,8,0,1,

%T 0,13,0,2,1,10,0,3,0,12,5,0,0,14,1,0,0,13,0,7,0,18,3,2,1,15,0,0,7,17,

%U 0,0,0,19,1,5,0,29,0,1,0,23,0,2,1,20,9,0,0,28,0,0,3,24,1,10,0,23,0,1,5,28,0

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

%H Seiichi Manyama, <a href="/A363900/b363900.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t a[n_] := DivisorSum[n, # &, Mod[n/#, 5] == 4 &]; Array[a, 100] (* _Amiram Eldar_, Jun 27 2023 *)

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

%Y Cf. A363897, A363898, A363899.

%Y Cf. A001899, A284103.

%K nonn

%O 1,8

%A _Seiichi Manyama_, Jun 27 2023