A364085 - OEIS

%I #12 Jul 05 2023 01:45:00

%S 1,2,3,5,5,6,8,8,11,11,11,12,14,17,15,19,17,18,24,20,21,23,25,29,29,

%T 26,27,29,35,32,32,32,33,46,35,39,40,38,47,41,41,42,49,55,45,47,50,48,

%U 64,50,53,59,53,65,56,56,57,64,71,60,69,67,63,82,67,66,68,68,86,79,71,74,74,89,81,77,77,78

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

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

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

%t a[n_] := DivisorSum[4*n - 1, # + 1 &, Mod[#, 4] == 3 &]/4; Array[a, 100] (* _Amiram Eldar_, Jul 05 2023 *)

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

%Y Cf. A364063, A364066.

%Y Cf. A078703.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jul 04 2023