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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Odd perfect numbers have at least nine distinct prime factors


Author: Pace P. Nielsen
Journal: Math. Comp. 76 (2007), 2109-2126
MSC (2000): Primary 11N25; Secondary 11Y50
Published electronically: May 9, 2007
MathSciNet review: 2336286
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Abstract: An odd perfect number, $ N$, is shown to have at least nine distinct prime factors. If $ 3\nmid N$ then $ N$ must have at least twelve distinct prime divisors. The proof ultimately avoids previous computational results for odd perfect numbers.


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Additional Information

Pace P. Nielsen
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: pace_nielsen@hotmail.com

DOI: http://dx.doi.org/10.1090/S0025-5718-07-01990-4
PII: S 0025-5718(07)01990-4
Keywords: Abundant, deficient, odd perfect
Received by editor(s): April 1, 2006
Received by editor(s) in revised form: September 1, 2006
Published electronically: May 9, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.