%I #11 Jul 02 2023 09:01:00

%S 1,1,3,1,5,3,9,1,19,5,33,3,65,9,135,1,257,19,513,5,1035,33,2049,3,

%T 4101,65,8211,9,16385,135,32769,1,65571,257,131085,19,262145,513,

%U 524355,5,1048577,1035,2097153,33,4194455,2049,8388609,3,16777225,4101,33554691,65,67108865,8211,134217765,9

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

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

%F a(n) = Sum_{d|n, d odd} 2^((d-1)/2).

%t a[n_] := DivisorSum[n, 2^((#-1)/2) &, OddQ[#] &]; Array[a, 50] (* _Amiram Eldar_, Jul 02 2023 *)

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

%Y Cf. A001227, A364035.

%K nonn

%O 1,3

%A _Seiichi Manyama_, Jul 02 2023