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^(gamma-eps) [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. 64-94.
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Dec 07 2016
EXTENSIONS
More terms from Peter J. C. Moses, Dec 07 2016
STATUS
approved