Aliquot sequences

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1976
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Abstract
It has been conjectured that aliquot sequences (i.e. those sequences obtained by iterating the number theoretic function s(n) = a(n)-n, where a(n) denotes the sum of the divisors) starting with an even number, are almost all unbounded. In this thesis, this conjecture is supported by both theory, and numerical evidence. A proof due to Lenstra that there exists sequences which are monotone increasing for an arbitrarily large number of terms is given. The concept of average order is used toestimate the behavior of s(n)/n and what theory is known is used to design a model for these sequences using Markov chains. A new method of factoring called POLLARD-RHO is then used to generate data and the statistics are compared with the theoretical estimates of the model. The final chapter contains extensive tables which enable one to determine the behavior of any sequence starting with a value of n less than 100000.
Description
Bibliography: p. 140-143.
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Citation
Devitt, J. S. (1976). Aliquot sequences (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/21933