A050499 Nearest integer to n/log(n).

3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17

Offset: 2

Author

N. J. A. Sloane, Dec 27 1999

Keywords

• nonn

Comments

The prime number theorem states that the number of primes <= x is asymptotic to x/log(x).

n/log(n) = n*A002285/log_10(n). [Eric Desbiaux, Jun 27 2009]

Similar to floor(1/(1-x)) where x^n=1/n. - Jon Perry, Oct 29 2013

References

• Cf. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Theorem 6.

Links

• T. D. Noe, Table of n, a(n) for n=2..10000

Crossrefs

Cf. A000720, A050500, A050501.

Programs

JavaScript

for (i=1;i<100;i++) {
x=Math.pow(1/i,1/i);
document.write(Math.floor(1/(1-x))+", ");
}

Mathematica

Table[Round[n/Log[n]],{n,2,80}] (* Harvey P. Dale, Nov 03 2013 *)

PARI

a(n) = round(n/log(n)); \\ Michel Marcus, Jan 24 2025