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%I #30 Jan 02 2023 12:30:53
%S 12,14,15,20,24,28,33,34,35,42,48,54,55,56,62,63,69,70,76,77,78,84,85,
%T 86,87,88,90,93,94,95,96,99,102,104,105,108,110,111,112,118,119,120,
%U 122,123,124,125,129,130,132,141,142,143,148,150
%N Numbers k such that the iteration k -> (sigma(k)+phi(k))/2 terminates at a fraction later than at the first step.
%C Termination at the first step occurs if k>3 is a square or twice a square, i.e. if k is a term of A028982. So the sequence lists the numbers that end at a fraction but are not of one of these two forms.
%H Hugo Pfoertner, <a href="/A290001/b290001.txt">Table of n, a(n) for n = 1..101</a>
%H Hugo Pfoertner, <a href="/A290001/a290001.txt">Table of n, a(n) for n = 1..1136</a> (values above first 101 terms are only guesses)
%H N. J. A. Sloane, <a href="http://list.seqfan.eu/oldermail/seqfan/2017-September/017915.html">Iterating some number-theoretic functions</a>, Posting to Seqfan mailing list, Sep 3, 2017
%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)
%e 42 is in the sequence because the following iteration reaches an odd sigma(k):
%e k sigma(k) phi(k)
%e 42 96 12 k->(sigma(k)+phi(k))/2, (96+12)/2=54
%e 54 120 18 k->(sigma(k)+phi(k))/2, (120+18)/2=69
%e 69 96 44 ...
%e 70 144 24 ...
%e 84 224 24
%e 124 224 60
%e 142 216 70
%e 143 168 120 k->(sigma(k)+phi(k))/2, (168+120)/2=144
%e 144 403 48 sigma(144) is odd, iteration terminates
%Y Cf. A000010, A000203, A028982, A289997, A291790, A291791.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, Sep 03 2017
%E b-file curtailed beyond last certain value, moved other values to a-file. - _N. J. A. Sloane_, Oct 01 2017
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