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 A222313 #27 Sep 04 2018 09:18:26
%S A222313 1,2,3,5,6,15,17,33,41,55,57,65,70,105,129,257,273,385,561,897,969,
%T A222313 1001,1105,1353,1430,1785,2049,2145,2337,2665,3553,4097,4305,4745,
%U A222313 4845,5633,6105,6545,8193,8385
%N A222313 A222311 sorted and duplicates removed (conjectured).
%C A222313 Obtained by sorting and removing duplicates from the first 500 terms of A222311. There is no proof as yet that this list is complete up to 105. Only the first three terms shown are certain. Is there a proof that 4 cannot appear?
%H A222313 Cristian Cobeli, Mihai Prunescu, Alexandru Zaharescu, <a href="http://arxiv.org/abs/1511.04315">A growth model based on the arithmetic Z-game</a>, arXiv:1511.04315 [math.NT], 2015.
%H A222313 Cristian Cobeli, Alexandru Zaharescu, <a href="http://arxiv.org/abs/1411.1334">A game with divisors and absolute differences of exponents</a>, arXiv:1411.1334 [math.NT], 2014 (see page 12).
%t A222313 terms = 40; nmax0 = 5000;
%t A222313 seq[nmax_] := seq[nmax] = Union[Print[nmax]; Join[r = {1}, Table[Reverse[r = FoldList[#1*(#2/GCD[#1, #2]^2) & , n, r]], {n, 2, nmax}][[All, 1]]]][[1 ;; terms]];
%t A222313 seq[nmax = nmax0]; seq[nmax = 2 nmax]; While[seq[nmax] == seq[nmax/2], nmax = 2 nmax]; seq[nmax] (* _Jean-François Alcover_, Sep 04 2018, after _Ivan Neretin_ in A222310 *)
%Y A222313 Cf. A222310, A222311.
%K A222313 nonn,more
%O A222313 1,2
%A A222313 _N. J. A. Sloane_, Feb 16 2013
%E A222313 Corrected and extended using data from Cobeli et al., 2015. - _N. J. A. Sloane_, Aug 27 2016
%E A222313 More terms (computed from a list of 10000) from _Jean-François Alcover_, Sep 04 2018