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 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
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 sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 91-100. See Eq. (4.2).
CROSSREFS
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