

A279161


Define P = e^gamma*loglog(n) and Q = 3/loglog(n), where gamma is Euler's constant A001620. Then a(n) = phi(n)  ceiling(n/(P + Q)), where phi(n) is Euler's function A000010.


3



1, 1, 3, 1, 4, 2, 4, 2, 7, 1, 9, 3, 4, 4, 12, 2, 13, 3, 7, 5, 17, 2, 14, 6, 12, 5, 21, 1, 23, 9, 12, 8, 16, 4, 27, 9, 15, 7, 31, 2, 32, 10, 14, 12, 35, 5, 31, 9, 20, 12, 40, 6, 28, 11, 23, 15, 45, 3, 46, 16, 22, 18, 34, 5, 51, 17, 29, 8, 54, 8, 56, 20, 23, 19
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OFFSET

3,3


COMMENTS

The best known lower estimate for phi(n)is phi(n) > n/(P + Q), n >= 3 [Rosser and Schoenfeld] (and, for each eps > 0, there exist infinitely many n for which phi(n) < n/P', where in P' e^gamma is replaced by e^(gammaeps) [Landau]). So a(n) >= 0.


REFERENCES

E. Landau, Handbuch der Lehre yon der Verteilung der Primzahlen, 2 vols., Leipzig, Teubner, 1909. Reprinted in 1953 by Chelsea Publishing Co., New York.


LINKS

Peter J. C. Moses, Table of n, a(n) for n = 3..5002
J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers. Illinois J. Math. 6 (1962), pp. 6494.


PROG

(PARI) a(n)=my(LL=log(log(n)), P=LL*exp(Euler), Q=3/LL); eulerphi(n)  ceil(n/(P+Q)) \\ Charles R Greathouse IV, Dec 07 2016


CROSSREFS

Cf. A000010, A001620.
Sequence in context: A210722 A162341 A066728 * A222046 A066899 A309636
Adjacent sequences: A279158 A279159 A279160 * A279162 A279163 A279164


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Dec 07 2016


EXTENSIONS

More terms from Peter J. C. Moses, Dec 07 2016


STATUS

approved



