

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^(gammaeps). 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), 357372
J.L. Nicolas, Petites valeurs de la fonction d'Euler, J. Number Theory 17, no.3 (1983), 375388.
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



