A178965 a(n) = numerator of Sum_{k>=1} floor(n/k)/2^k.

0, 1, 5, 15, 43, 103, 263, 591, 1391, 3103, 7007, 15039, 33983, 72063, 156543, 334591, 722687, 1510911, 3255807, 6773759, 14433279, 30193663, 63535103, 131264511, 278589439, 575004671, 1200349183, 2484846591, 5189910527, 10648256511, 22287450111, 45648642047

Offset

0,3

Links

Jinyuan Wang, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{i=1..n} 2^(n-i)*floor(n/i). - Ridouane Oudra, Jul 30 2019

Example

a(3)=15 because Sum_{k>=1} floor(3/k)/2^k = 15/8.

Maple

seq(add(2^(n-i)*floor(n/i), i=1..n), n=0..60); # Ridouane Oudra, Jul 30 2019

Mathematica

Table[Numerator[Sum[Floor[n/k]/2^k, {k, 1, Infinity}]], {n, 0, 25}]

Prog

(Magma) [0] cat [&+[2^(n-i)*Floor(n/i):i in [1..n]]:n in [1..25]]; // Marius A. Burtea, Jul 30 2019
(PARI) a(n) = numerator(sum(k=1, n, floor(n/k)/2^k)); \\ Jinyuan Wang, Jul 31 2019

Crossrefs

Sequence in context: A111295 A200760 A032193 * A005665 A025471 A064453

Adjacent sequences: A178962 A178963 A178964 * A178966 A178967 A178968

Keyword

nonn,frac

Author

Vladimir Reshetnikov, Dec 31 2010

Status

approved