A345108 a(n) = Sum_{k=1..n} 2^(n - floor(n/k)).

1, 3, 9, 21, 57, 121, 305, 657, 1505, 3233, 7489, 15169, 34433, 72833, 156929, 325889, 717313, 1462785, 3187713, 6538241, 13846529, 28739585, 61673473, 124063745, 263856129, 544481281, 1139032065, 2326282241, 4920999937, 9924804609, 20923351041, 42635165697

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..3000

Formula

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

Mathematica

a[n_] := Sum[2^(n - Floor[n/k]), {k, 1, n}]; Array[a, 30] (* Amiram Eldar, Jun 08 2021 *)

Prog

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

Crossrefs

Cf. A345028, A345109.

Sequence in context: A272265 A191796 A367111 * A007056 A026551 A296719

Adjacent sequences: A345105 A345106 A345107 * A345109 A345110 A345111

Keyword

nonn

Author

Seiichi Manyama, Jun 08 2021

Status

approved