This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A089684 #26 Dec 01 2024 04:09:54
%S A089684 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,
%T A089684 49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,
%U A089684 95,97,99,101,103,107,109,111,113,115,117,119,121,123,125,127
%N A089684 Numbers k such that 2*phi(k) > k.
%H A089684 Amiram Eldar, <a href="/A089684/b089684.txt">Table of n, a(n) for n = 1..10000</a>
%H A089684 Amiram Eldar, <a href="/A089684/a089684_1.jpg">Plot of a(n)/n for n = 2^(20..34)</a>.
%H A089684 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 A089684 Vaclav Kotesovec, <a href="/A089684/a089684.jpg">Plot of a(n)/n for n = 1..1000000</a>.
%F A089684 Asymptotic to c*n with c = 2.045...
%F A089684 2.04582 < c < 2.04818 (from the bounds on the asymptotic density of A119432 given by Kobayashi, 2016). - _Amiram Eldar_, Dec 01 2024
%t A089684 lst={}; Do[If[2*EulerPhi[n]>n, AppendTo[lst, n]], {n, 200}]; lst (* _T. D. Noe_ *)
%t A089684 Select[ Range[130], 2EulerPhi[ # ] > # &] (* _Robert G. Wilson v_, Jan 16 2004 *)
%o A089684 (PARI) is(k) = 2*eulerphi(k) > k; \\ _Amiram Eldar_, Dec 01 2024
%Y A089684 Cf. A000010, A036798, A067800 (nonprime n such that phi(n) > n/2).
%Y A089684 Cf. A036798, the missing odd numbers.
%Y A089684 Complement of A119432.
%K A089684 nonn,easy
%O A089684 1,2
%A A089684 _Benoit Cloitre_, Jan 16 2004