Aliquot sequences
| dc.contributor.advisor | Guy, Richard K. | |
| dc.contributor.author | Devitt, John Stanley | |
| dc.date.accessioned | 2005-07-19T20:00:54Z | |
| dc.date.available | 2005-07-19T20:00:54Z | |
| dc.date.issued | 1976 | |
| dc.description | Bibliography: p. 140-143. | en |
| dc.description.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. | |
| dc.description.notes | This title is not available online. Access options are: - consulting the copy from Archives in our reading room in person - https://asc.ucalgary.ca/visiting/ - borrowing a circulating copy from the Library catalogue – https://ucalgary.primo.exlibrisgroup.com/discovery/search?vid=01UCALG_INST:UCALGARY&lang=en | |
| dc.format.extent | ix, 143 leaves : ill. ; 30 cm. | en |
| dc.identifier | 82480955 | en |
| dc.identifier.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 | en_US |
| dc.identifier.doi | http://dx.doi.org/10.11575/PRISM/21933 | |
| dc.identifier.lcc | QA 292 D48 1976 Microfiche | en |
| dc.identifier.other | 82480955 | en |
| dc.identifier.uri | http://hdl.handle.net/1880/13124 | |
| dc.language.iso | eng | |
| dc.publisher.institution | University of Calgary | en |
| dc.publisher.place | Calgary | en |
| dc.rights | University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. | |
| dc.subject.lcc | QA 292 D48 1976 Microfiche | en |
| dc.subject.lcsh | Sequences (Mathematics) | |
| dc.title | Aliquot sequences | |
| dc.type | master thesis | |
| thesis.degree.discipline | Mathematics and Statistics | |
| thesis.degree.grantor | University of Calgary | |
| thesis.degree.name | Master of Science (MSc) | |
| ucalgary.thesis.accession | Theses Collection 58.002:Box 255 82480955 | |
| ucalgary.thesis.notes | PL | en |
| ucalgary.thesis.uarcrelease | no | en |