A037229 n such that pi(n) >= phi(n).

2, 3, 4, 6, 8, 10, 12, 14, 18, 20, 24, 30, 42, 60, 90

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• fini
• full

Comments

It is known (see references) that, for n>15, phi(n)>n/(e^c*log(log(n))+3) and pi(n)<1.25506*n/log(n), where c is the Euler constant. Therefore, there are no terms, at least, for n satisfying the inequality: log(n)/(e^c*log(log(n))+3)>1.25506... So, for, e.g., n>=5500, there are no terms. Besides, by the direct verification, we find that interval (90,5500) contains no terms as well. - Vladimir Shevelev, Aug 27 2011

References

• N. E. Bach, J. Shallit, Algorithmic Number Theory, MIT Press, 233 (1996). ISBN 0-262-02405-5 (Theorem 8.8.7)

Links

• J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. Journ. Math. 6 (1962) 64-94.

Crossrefs

Cf. A000010, A000720, A037171, A037228, A073464.