A163568 Floor of the integral of x/log(x) for x=2 to 10^n.

27, 1243, 78624, 5762206, 455055611, 37607950277, 3204942065688, 279238344248553, 24739954309690412, 2220819602783663480, 201467286691248261495, 18435599767366347775141, 1699246750872593033005720, 157589269275974838158399968, 14692398897720447639079087666

Offset: 1

Author

Cino Hilliard, Jul 30 2009

Keywords

• nonn

Comments

This integral is an approximation to the sum of x/log(x) for x=2 to 10^n and closely approximates Pi(n^2) for x = 2 to n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A163521.

Programs

Mathematica

Table[Floor[NIntegrate[x/Log[x], {x, 2, 10^n}]], {n, 1, 10}] (* G. C. Greubel, Jul 28 2017 *)

PARI

g(n)=intnum(x=2,10^n,x/log(x)); for(x=1,20,print1(floor(g(x))","))

Extensions

Edited (but not checked) by N. J. A. Sloane, Aug 01 2009

Offset and upper limit in the definition corrected by R. J. Mathar, Aug 02 2009