A359733 - OEIS

%I #16 Aug 14 2023 02:00:21

%S 1,4,7,20,21,88,71,296,373,1084,1035,5084,4109,16496,20787,67728,

%T 65553,286516,262163,1070180,1189937,4194568,4194327,17760824,

%U 16827241,67109228,72150655,269503660,268435485,1104603808,1073741855,4303389216,4476371181

%N a(n) = (1/2) * Sum_{d|n} (2*d)^(n/d).

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

%t a[n_] := DivisorSum[n, (2*#)^(n/#) &] / 2; Array[a, 33] (* _Amiram Eldar_, Aug 14 2023 *)

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

%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-2*k*x^k)))

%Y Cf. A055225, A076717.

%K nonn,easy

%O 1,2

%A _Seiichi Manyama_, Jan 12 2023