|
%I #12 Jun 30 2023 15:37:03
%S 0,1,0,1,4,1,0,10,0,5,16,1,0,26,4,10,36,1,0,54,0,17,64,10,4,82,0,26,
%T 100,5,0,131,16,37,148,1,0,170,0,63,196,26,0,242,4,65,256,10,0,294,36,
%U 82,324,1,20,396,0,101,400,54,0,442,0,131,488,17,0,566,64,174,576,10,0,626,4,170
%N Expansion of Sum_{k>0} k^2 * x^(3*k-1) / (1 - x^(3*k-1)).
%F a(n) = Sum_{d|n, d==2 mod 3} ((d+1)/3)^2.
%t a[n_] := DivisorSum[n, ((#+1)/3)^2 &, Mod[#, 3] == 2 &]; Array[a, 100] (* _Amiram Eldar_, Jun 30 2023 *)
%o (PARI) a(n) = sumdiv(n, d, (d%3==2)*((d+1)/3)^2);
%Y Cf. A001822, A363902.
%Y Cf. A103638, A363976.
%K nonn,easy
%O 1,5
%A _Seiichi Manyama_, Jun 30 2023
|
