A141602 Integer part of 2^n/log(2^n).

2, 2, 3, 5, 9, 15, 26, 46, 82, 147, 268, 492, 909, 1688, 3151, 5909, 11123, 21010, 39809, 75638, 144073, 275050, 526182, 1008516, 1936352, 3723754, 7171675, 13831089, 26708310, 51636066, 99940774, 193635250, 375535031, 728979766, 1416303547

Offset: 1

Author

Cino Hilliard, Aug 21 2008

Keywords

• nonn

Comments

2^n/log(2^n) is an approximation to the number of primes < 2^n.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000799, A007525, A050500, A185192.

Programs

Magma

A141602:= func< n | Floor(2^n/(n*Log(2))) >;
[A141602(n): n in [1..40]]; // G. C. Greubel, Sep 21 2024

Mathematica

Floor[2^#/Log[2^#]]&/@Range[40] (* Harvey P. Dale, Mar 11 2013 *)

PARI

g(n) = for(x=1,n,y=floor(2^x/log(2^x));print1(y","))

PARI

a(n) = 2^n\log(2^n); \\ Michel Marcus, Feb 24 2021

SageMath

def A141602(n): return int(2^n/(n*log(2)))
[A141602(n) for n in range(1,41)] # G. C. Greubel, Sep 21 2024

Formula

a(n) = A050500(2^n) = floor(2^n*A007525/n) >= A000799(n). - R. J. Mathar, Jan 05 2009