A037229 Numbers k such that pi(k) >= phi(k).

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

Offset

0,1

Comments

It is known (see references) that, for k>15, phi(k)>k/(e^c*log(log(k))+3) and pi(k)<1.25506*k/log(k), where c is the Euler constant. Therefore, there are no terms, at least, for k satisfying the inequality: log(k)/(e^c*log(log(k))+3)>1.25506... So, for, e.g., k>=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

Table of n, a(n) for n=0..14.

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.

Sequence in context: A122957 A078769 A064375 * A351740 A230374 A396379

Adjacent sequences: A037226 A037227 A037228 * A037230 A037231 A037232

Keyword

nonn,fini,full

Author

David W. Wilson

Status

approved