A364096 - OEIS

%I #17 Jul 12 2023 01:01:01

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

%H Seiichi Manyama, <a href="/A364096/b364096.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

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

%Y Cf. A359233, A364092.

%Y Cf. A363028, A363155, A364104.

%K nonn

%O 1,5

%A _Seiichi Manyama_, Jul 04 2023