

A037229


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


2



2, 3, 4, 6, 8, 10, 12, 14, 18, 20, 24, 30, 42, 60, 90
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

It is known (see references) that, for n>15, phi(n)>n/(e^c*ln(ln(n))+3) and pi(n)<1.25506*n/ln(n), where c is the Euler constant. Therefore, there are no terms, at least, for n satisfying the inequality: ln(n)/(e^c*ln(ln(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 0262024055 (Theorem 8.8.7)
J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 6497.


LINKS

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


CROSSREFS

Sequence in context: A122957 A078769 A064375 * A230374 A007183 A067783
Adjacent sequences: A037226 A037227 A037228 * A037230 A037231 A037232


KEYWORD

nonn,fini,full


AUTHOR

David W. Wilson


STATUS

approved



