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 A119432 Numbers k such that 2*phi(k) <= k. 4
 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, numbers k such that totient(k) <= cototient(k). Using the primes up to 23 it is possible to show that this sequence has (lower) density greater than 0.51. - Charles R Greathouse IV, Oct 26 2015 The asymptotic density of this sequence is in the interval (0.51120, 0.51176) (Kobayashi, 2016, improving the bounds 0.5105 and 0.5241 that were given by Wall, 1972). - Amiram Eldar, Oct 15 2020 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Mitsuo Kobayashi, A generalization of a series for the density of abundant numbers, International Journal of Number Theory, Vol. 12, No. 3 (2016), pp. 671-677. Charles R. Wall, Density bounds for Euler's function, Mathematics of Computation, Vol. 26, No. 119 (1972), pp. 779-783. FORMULA Elements of A054741 together with all 2^n for n>0. MATHEMATICA Select[Range[130], 2*EulerPhi[#] <= # &] (* Amiram Eldar, Feb 29 2020 *) PROG (PARI) is(n)=2*eulerphi(n)<=n \\ Charles R Greathouse IV, Oct 26 2015 CROSSREFS Disjoint union of A119434 and A299174. - Amiram Eldar, Oct 15 2020 Cf. A000010, A054741, A119433. Sequence in context: A055966 A087113 A004275 * A005843 A317108 A317440 Adjacent sequences:  A119429 A119430 A119431 * A119433 A119434 A119435 KEYWORD nonn AUTHOR Franklin T. Adams-Watters, May 19 2006 STATUS approved

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Last modified June 12 22:32 EDT 2021. Contains 344973 sequences. (Running on oeis4.)