Finite connected components of the aliquot graph

Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than 10^9, as well as those containing an amicable pair below 10^{14} or one of the known perfect or sociable cycles below 10^{17}. Along the way we dev...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics of computation 2018-11, Vol.87 (314), p.2891-2902
Main Author: BOOKER, ANDREW R.
Format: Article
Language:English
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than 10^9, as well as those containing an amicable pair below 10^{14} or one of the known perfect or sociable cycles below 10^{17}. Along the way we develop a fast algorithm for computing the inverse image of an even number under the sum-of-proper-divisors function.
ISSN:0025-5718
1088-6842
DOI:10.1090/mcom/3299