Finite connected components of the aliquot graph
Number Theory
2017-06-16 v2
Abstract
Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than , as well as those containing an amicable pair below or one of the known perfect or sociable cycles below . Along the way we develop a fast algorithm for computing the inverse image of an even number under the sum-of-proper-divisors function.
Keywords
Cite
@article{arxiv.1610.07471,
title = {Finite connected components of the aliquot graph},
author = {Andrew R. Booker},
journal= {arXiv preprint arXiv:1610.07471},
year = {2017}
}
Comments
10 pages, to appear in Mathematics of Computation