A363970 - OEIS

%I #11 Jun 30 2023 15:37:12

%S 1,1,1,5,1,1,10,5,1,17,1,5,26,10,1,41,1,1,50,21,10,65,1,5,82,26,1,114,

%T 1,17,122,41,1,145,10,5,170,50,26,217,1,10,226,69,1,257,1,41,299,98,1,

%U 354,1,1,362,114,50,401,1,21,442,122,10,525,26,65,530,149,1,602,1,5,626,170

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

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

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

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

%Y Cf. A001817, A363901.

%Y Cf. A103637, A363975.

%K nonn,easy

%O 1,4

%A _Seiichi Manyama_, Jun 30 2023