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A037229
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n such that pi(n) >= phi(n).
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2
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2, 3, 4, 6, 8, 10, 12, 14, 18, 20, 24, 30, 42, 60, 90
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OFFSET
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0,1
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=0..14.
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CROSSREFS
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Sequence in context: A122957 A078769 A064375 * A230374 A007183 A067783
Adjacent sequences: A037226 A037227 A037228 * A037230 A037231 A037232
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KEYWORD
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nonn,fini,full
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AUTHOR
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David W. Wilson
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STATUS
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approved
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