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A119432 Numbers k such that 2*phi(k) <= k.

%I A119432 #17 Oct 15 2020 03:58:58
%S A119432 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,
%T A119432 50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,
%U A119432 96,98,100,102,104,105,106,108,110,112,114,116,118,120,122,124,126,128,130
%N A119432 Numbers k such that 2*phi(k) <= k.
%C A119432 Equivalently, numbers k such that totient(k) <= cototient(k).
%C A119432 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
%C A119432 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
%H A119432 Amiram Eldar, <a href="/A119432/b119432.txt">Table of n, a(n) for n = 1..10000</a>
%H A119432 Mitsuo Kobayashi, <a href="https://doi.org/10.1142/S1793042116500445">A generalization of a series for the density of abundant numbers</a>, International Journal of Number Theory, Vol. 12, No. 3 (2016), pp. 671-677.
%H A119432 Charles R. Wall, <a href="https://doi.org/10.1090/S0025-5718-1972-0327701-9">Density bounds for Euler's function</a>, Mathematics of Computation, Vol. 26, No. 119 (1972), pp. 779-783.
%F A119432 Elements of A054741 together with all 2^n for n>0.
%t A119432 Select[Range[130], 2*EulerPhi[#] <= # &] (* _Amiram Eldar_, Feb 29 2020 *)
%o A119432 (PARI) is(n)=2*eulerphi(n)<=n \\ _Charles R Greathouse IV_, Oct 26 2015
%Y A119432 Disjoint union of A119434 and A299174. - _Amiram Eldar_, Oct 15 2020
%Y A119432 Cf. A000010, A054741, A119433.
%K A119432 nonn
%O A119432 1,1
%A A119432 _Franklin T. Adams-Watters_, May 19 2006