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.

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

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

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