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A100966 Values of k such that EulerPhi(k) < k/(exp(EulerGamma)*log(log(k))). 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
From Vladimir Shevelev, Dec 08 2016: (Start)
Define P = exp(gamma)*log(log(k)), where gamma is Euler's constant A001620. The sequence lists numbers k for which phi(k) < k/P, where phi(k) is Euler's function A000010.
In 1909, Landau proved that for each eps>0, there exist infinitely many k for which phi(k) < k/P', where P' = exp(gamma-eps)*log(log(k)). In 1983 Nicolas strengthened Landau's result showing that there exist infinitely many k for which phi(k) < k/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
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 and 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 * A358973 A063977 A290136
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 March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)