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Statistical Analysis of Aliquot Sequences Jacobson, Jr., Michael
Description
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 Metadata
| Title |
Statistical Analysis of Aliquot Sequences
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2020-05-03T10:50
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| Description |
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.
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| Extent |
39.0 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: University of Calgary
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| Series | |
| Date Available |
2020-10-31
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0394885
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Faculty
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International