

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.


6



1, 2, 5, 16, 19, 27, 29, 33, 49, 50, 52, 66, 81, 85, 105, 146, 147, 163, 170, 189, 197, 199, 218, 226, 243, 262, 303, 315, 343, 424, 430, 438, 453, 461, 463, 469, 472, 484, 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
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OFFSET

1,2


COMMENTS

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.
The thousandterm bfile (up to 141441) has been checked to correspond to disjoint trees for 265 iterations of sigma on each term, and every nonterm n < 141441 merges (in at most 21 iterations) with an earlier iteration sequence.  Hans Havermann, Nov 22 2019
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


REFERENCES

Kerry Mitchell, Posting to Math Fun Mailing List, Apr 30 2015


LINKS

Hans Havermann, Table of n, a(n) for n = 1..1000
G. L. Cohen and H. J. J. te Riele, Iterating the sumofdivisors function, Experimental Mathematics, 5 (1996), pp. 91100. See Eq. (4.2).


CROSSREFS

Cf. A000203 (sigma), A007497 (trajectory of 2), A051572 (trajectory of 5), A257349 (trajectory of 16).
Cf. A216200 (number of disjoint trees up to n); A257669 and A257670: size and smallest number of subtree rooted in n.
Sequence in context: A286382 A127580 A098048 * A101847 A251600 A117557
Adjacent sequences: A257345 A257346 A257347 * A257349 A257350 A257351


KEYWORD

nonn,hard


AUTHOR

N. J. A. Sloane, May 01 2015, following a suggestion from Kerry Mitchell.


EXTENSIONS

More terms from Hans Havermann, May 02 2015


STATUS

approved



