%N Numbers whose trajectory under iteration of the map k -> (sigma(k)+phi(k))/2 consists only of integers and is unbounded.
%C It would be nice to have a proof that these trajectories are integral and unbounded, or, of course, that they eventually reach a fractional value (and die), or reach a prime (which is then a fixed point). (Cf. A291787.) If either of the last two things happen, then that value of n will be removed from the sequence. AT PRESENT ALL TERMS ARE CONJECTURAL.
%C When this sequence was submitted, there was a hope that it would be possible to prove that these trajectories were indeed integral and unbounded. This has not yet happened, although see the remarks of _Andrew R. Booker_ in A292108. - _N. J. A. Sloane_, Sep 25 2017
%H Hugo Pfoertner, <a href="/A291790/b291790.txt">Table of n, a(n) for n = 1..82</a>
%H Sean A. Irvine, <a href="/A291790/a291790.png">Showing how the initial portions of some of these trajectories merge</a>
%H N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, <a href="https://vimeo.com/237029685">Part I</a>, <a href="https://vimeo.com/237030304">Part 2</a>, <a href="https://oeis.org/A290447/a290447_slides.pdf">Slides.</a> (Mentions this sequence)
%Y Cf. A000010, A000203, A289997, A290001, A291789 (the trajectory of 270), A291787, A292108.
%Y For the "seeds" see A292766.
%A _N. J. A. Sloane_, Sep 03 2017
%E More terms from _Hugo Pfoertner_, Sep 03 2017