A359206 a(n) = Sum_{d|n} 4^(n-d).

1, 5, 17, 81, 257, 1345, 4097, 20737, 69633, 328705, 1048577, 5574657, 16777217, 83902465, 286261249, 1359020033, 4294967297, 22565617665, 68719476737, 348967141377, 1168499539969, 5497562333185, 17592186044417, 93531519582209, 282574488338433

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, 4^(n-#) &]; Array[a, 25] (* Amiram Eldar, Aug 23 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, 4^(n-d));
(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)))
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(4*x)^k)))

Crossrefs

Cf. A074854, A112329, A357051.

Cf. A342628, A342629, A359204.

Sequence in context: A369262 A053418 A151882 * A149749 A149750 A179605

Adjacent sequences: A359203 A359204 A359205 * A359207 A359208 A359209

Keyword

nonn

Author

Seiichi Manyama, Dec 20 2022

Status

approved