Mathematics of Computation

Author(s): Pace P. Nielsen.
Journal: Math. Comp. 76 (2007), 2109-2126.
MSC (2000): Primary 11N25; Secondary 11Y50
Posted: May 9, 2007
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Abstract: An odd perfect number,

, is shown to have at least nine distinct prime factors. If $3\nmid N$ then

must have at least twelve distinct prime divisors. The proof ultimately avoids previous computational results for odd perfect numbers.

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

DOI: 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
Posted: May 9, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN 1088-6842(e) ISSN 0025-5718(p)

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