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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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified August 12 02:46 EDT 2020. Contains 336436 sequences. (Running on oeis4.)