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A100966
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Values of k such that EulerPhi(k) < k/(exp(EulerGamma)*log(log(k))).
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3
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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
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OFFSET
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1,1
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COMMENTS
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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)
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REFERENCES
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E. Landau, Handbuch der Lehre yon der Verteilung der Primzahlen, 2 vols., Leipzig, Teubner, 1909. Reprinted in 1953 by Chelsea Publishing Co., New York.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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