A359190 - OEIS

%I #13 Aug 27 2023 17:03:15

%S 1,6,19,76,261,1074,4103,16536,65593,262686,1048587,4196644,16777229,

%T 67117098,268436319,1073774896,4294967313,17180003478,68719476755,

%U 274878432636,1099511640197,4398048608322,17592186044439,70368752620104,281474976711961,1125899940397134

%N a(n) = Sum_{d|n} d * 4^(n/d-1).

%F G.f.: Sum_{k>=1} k * x^k/(1 - 4 * x^k).

%F G.f.: Sum_{k>=1} 4^(k-1) * x^k/(1 - x^k)^2.

%t a[n_] := DivisorSum[n, 4^(n/#-1)*# &]; Array[a, 26] (* _Amiram Eldar_, Aug 27 2023 *)

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-4*x^k)))

%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, 4^(k-1)*x^k/(1-x^k)^2))

%Y Cf. A054599, A359189.

%K nonn,easy

%O 1,2

%A _Seiichi Manyama_, Dec 19 2022