A363972 - OEIS

%I #13 Jun 30 2023 15:36:39

%S 1,1,1,1,5,1,1,1,10,5,1,1,17,1,5,1,26,10,1,5,37,1,1,1,54,17,10,1,65,5,

%T 1,1,82,26,5,10,101,1,17,5,122,37,1,1,158,1,1,1,170,54,26,17,197,10,5,

%U 1,226,65,1,5,257,1,46,1,310,82,1,26,325,5,1,10,362,101,54,1,401,17,1,5,451,122,1

%N Expansion of Sum_{k>0} k^2 * x^(4*k-3) / (1 - x^(4*k-3)).

%F a(n) = Sum_{d|n, d==1 mod 4} ((d+3)/4)^2.

%t a[n_] := DivisorSum[n, ((#+3)/4)^2 &, Mod[#, 4] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jun 30 2023 *)

%o (PARI) a(n) = sumdiv(n, d, (d%4==1)*((d+3)/4)^2);

%Y Cf. A001826, A363903.

%Y Cf. A050450, A363977.

%K nonn,easy

%O 1,5

%A _Seiichi Manyama_, Jun 30 2023