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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 24 20:35 EDT 2021. Contains 348233 sequences. (Running on oeis4.)