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A100966 Values of n such that EulerPhi(n) < n/(exp(EulerGamma)*log(log(n))). 3
3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 36, 40, 42, 48, 50, 54, 60, 66, 70, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 140, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Comments from  Vladimir Shevelev, Dec 08 2016 (Start):

Define P=e^gamma*loglog(n), where gamma is Euler's constant A001620. The sequence lists numbers n for which phi(n) < n/P, where phi(n) is Euler's function A000010.

In 1909, Landau proved that 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). In 1983 Nicolas strengthened Landau's result showing that there exist infinitely many n for which phi(n) < n/P. So this sequence is infinite.

All terms are even, except for 3,5,9 and 15. See proof in [Choie et al., Theorem 2.1].

(End)

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

T. D. Noe and Peter J. C. Moses, Table of n, a(n) for n = 1..5000 [First 2357 terms from T. D. Noe]

Y. Choie, N. Lichiardopol, P. Moree, P. Sole, On Robin's criterion for the Riemann hypothesis J. Theor. Nombr. Bord. 19 (2) (2007), 357-372

J.-L. Nicolas, Petites valeurs de la fonction d'Euler, J. Number Theory 17, no.3 (1983), 375-388.

Eric Weisstein's World of Mathematics, Totient Function

CROSSREFS

Superset of A227243.

Cf. A000010 (phi), A001620 (gamma), A279161.

Sequence in context: A001957 A184484 A253897 * A063977 A290136 A306588

Adjacent sequences:  A100963 A100964 A100965 * A100967 A100968 A100969

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Nov 23 2004

EXTENSIONS

Edited by N. J. A. Sloane, Jan 04 2017

STATUS

approved

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Last modified August 26 00:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)