BIRS Workshop Lecture Videos
Statistical Analysis of Aliquot Sequences Jacobson, Jr., Michael
Let $s(n) = \sigma(n) - n$ denote the proper sum of divisors function. In his 1976 M.Sc. thesis, Stan Devitt (supervised by Richard Guy) presented theoretical and numerical evidence, using a ``new method of factoring called POLLARD-RHO'', that the average order of $s(n)/n$ in successive iterations of $s(n)$ (Aliquot sequences) is greater than 1. These results seemingly lent support to the Guy/Selfridge Conjecture that there exist unbounded Aliquot sequences. In this talk, we describe the results of a project suggested by Richard in his efforts to provide more evidence in support of the Guy/Selfridge conjecture. In particular, we expand and update Devitt's computations by considering the more-appropriate geometric mean of $s(n)/n$ as opposed to the arithmetic mean considered by Devitt, and greatly extending Devitt's computations using modern factoring algorithms. This is joint work with K. Chum, R. Guy, and A. Mosunov.
Item Citations and Data
Attribution-NonCommercial-NoDerivatives 4.0 International