Odd perfect numbers have at least nine distinct prime factors
Abstract
An odd perfect number, N , is shown to have at least nine distinct prime factors. If 3nmid N then N must have at least twelve distinct prime divisors. The proof ultimately avoids previous computational results for odd perfect numbers.
 Publication:

Mathematics of Computation
 Pub Date:
 December 2007
 DOI:
 10.1090/S0025571807019904
 arXiv:
 arXiv:math/0602485
 Bibcode:
 2007MaCom..76.2109N
 Keywords:

 Abundant;
 deficient;
 odd perfect;
 Mathematics  Number Theory;
 11N25;
 11Y50
 EPrint:
 17 pages