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 A257348 #50 Jul 09 2025 04:39:40 %S A257348 1,2,5,16,19,27,29,33,49,50,52,66,81,85,105,146,147,163,170,189,197, %T A257348 199,218,226,243,262,303,315,343,424,430,438,453,461,463,469,472,484, %U A257348 489,513,530,550,584,677,722,746,786,787,804,813,821,831,842,859,867,876,892,903,914,916,937,977,982,988,990,1029 %N A257348 Repeatedly applying the map x -> sigma(x) partitions the natural numbers into a number of disjoint trees; sequence gives the (conjectural) list of minimal representatives of these trees. %C A257348 Very little is known for certain. Even the trajectories of 2 (A007497) and 5 (A051572) under repeated application of the map x -> sigma(x) (cf. A000203) are only conjectured to be disjoint. %C A257348 The thousand-term b-file (up to 141441) has been checked to correspond to disjoint trees for 265 iterations of sigma on each term, and every non-term n < 141441 merges (in at most 21 iterations) with an earlier iteration sequence. - _Hans Havermann_, Nov 22 2019 %C A257348 Rather than trees we mean connected components of the graphs with edges x -> sigma(x). The number 1 is a fixed point, i.e., a cycle of length 1 under iterations of sigma, it is not part of a tree. But since sigma(n) > n for n > 1 there are no other cycles. - _M. F. Hasler_, Nov 21 2019 %D A257348 Kerry Mitchell, Posting to Math Fun Mailing List, Apr 30 2015 %H A257348 Hans Havermann, <a href="/A257348/b257348.txt">Table of n, a(n) for n = 1..1000</a> %H A257348 G. L. Cohen and H. J. J. te Riele, <a href="http://projecteuclid.org/euclid.em/1047565640">Iterating the sum-of-divisors function</a>, Experimental Mathematics, 5 (1996), pp. 91-100. See Eq. (4.2). %Y A257348 Cf. A000203 (sigma), A007497 (trajectory of 2), A051572 (trajectory of 5), A257349 (trajectory of 16). %Y A257348 Cf. A216200 (number of disjoint trees up to n); A257669 and A257670: size and smallest number of subtree rooted in n. %K A257348 nonn,hard %O A257348 1,2 %A A257348 _N. J. A. Sloane_, May 01 2015, following a suggestion from _Kerry Mitchell_ %E A257348 More terms from _Hans Havermann_, May 02 2015