A364098 - OEIS

%I #12 Jul 12 2023 01:01:09

%S 1,1,3,1,4,1,5,1,8,1,7,1,8,1,11,4,10,1,11,1,14,1,17,1,14,1,20,1,16,6,

%T 17,1,20,1,19,1,26,4,27,1,22,1,23,8,26,1,25,1,29,1,42,1,28,1,33,1,32,

%U 10,31,4,32,1,41,1,44,1,35,1,38,1,44,17,38,1,48,1,40,1,53,1,44,4,43,1,44,14,59,1

%N Expansion of Sum_{k>0} k * x^(2*k-1) / (1 - x^(5*k-4)).

%F a(n) = (1/5) * Sum_{d | 5*n-3, d==1 (mod 5)} (d+4).

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

%t a[n_] := DivisorSum[5*n - 3, # + 4 &, Mod[#, 5] == 1 &]/5; Array[a, 100] (* _Amiram Eldar_, Jul 12 2023 *)

%o (PARI) a(n) = sumdiv(5*n-3, d, (d%5==1)*(d+4))/5;

%Y Cf. A359237, A364094.

%K nonn

%O 1,3

%A _Seiichi Manyama_, Jul 04 2023