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 A291934 #10 Sep 06 2017 21:18:46
%S A291934 1,2,3,4,5,7,7,8,9,11,11,16,13,16,16,16,17,18,19,25,23,23,23,36,25,29,
%T A291934 29,36,29,53,31,32,36,36,36,36,37,53,53,53,41,144,43,61,61,47,47,144,
%U A291934 49,50,61,61,53,144,72,72,59,59,59,107,61,144
%N A291934 Largest k achievable by the iteration k->(sigma(k)+phi(k))/2 started at k=n, with termination when sigma(k) becomes odd.
%C A291934 See A291914 for types of termination. The first term with unknown conjecturally unbounded behavior is a(270). More values of n with this type of behavior are given in A291790.
%C A291934 All bounded terms of this sequence are either prime or in A028982.
%H A291934 Hugo Pfoertner, <a href="/A291934/b291934.txt">Table of n, a(n) for n = 1..269</a>
%H A291934 Hugo Pfoertner, <a href="/A291934/a291934.pdf">Illustration of sequence terms for n<=5000</a>, omitting n in A291790.
%e A291934 a(38)=53: Starting with k=38 produces the trajectory 38 -> 39 -> 50 -> 53 -> 53 ...
%e A291934 a(42)=144: See example in A290001.
%t A291934 With[{lim = 100}, TakeWhile[#, # > 0 &] &@ Table[Which[Length@ # < lim, Last@ #, SameQ @@ Take[#, -2], Last@ #, True, 0] &@ NestWhileList[(DivisorSigma[1, #] + EulerPhi[#])/2 &, n, EvenQ@ DivisorSigma[1, #] &, 1, lim], {n, 270}]] (* _Michael De Vlieger_, Sep 06 2017 *)
%Y A291934 CF. A000010, A000040, A000203, A028982, A289997, A290001, A291789, A291790, A291791, A291914.
%K A291934 nonn
%O A291934 1,2
%A A291934 _Hugo Pfoertner_, Sep 06 2017