A359206 - OEIS

%I #11 Aug 23 2023 08:42:19

%S 1,5,17,81,257,1345,4097,20737,69633,328705,1048577,5574657,16777217,

%T 83902465,286261249,1359020033,4294967297,22565617665,68719476737,

%U 348967141377,1168499539969,5497562333185,17592186044417,93531519582209,282574488338433

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

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

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

%t a[n_] := DivisorSum[n, 4^(n-#) &]; Array[a, 25] (* _Amiram Eldar_, Aug 23 2023 *)

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

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

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

%Y Cf. A074854, A112329, A357051.

%Y Cf. A342628, A342629, A359204.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Dec 20 2022