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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 0-262-02405-5 (Theorem 8.8.7)

J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-97.

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

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Last modified September 2 23:10 EDT 2014. Contains 246369 sequences.