|
| |
|
|
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; 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.
|
|
|
CROSSREFS
| Sequence in context: A122957 A078769 A064375 * A007183 A067783 A062418
Adjacent sequences: A037226 A037227 A037228 * A037230 A037231 A037232
|
|
|
KEYWORD
| nonn,fini,full
|
|
|
AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
|
| |
|
|
