Odd perfect numbers have at least nine distinct prime factors

@article{Nielsen2007OddPN,
  title={Odd perfect numbers have at least nine distinct prime factors},
  author={Pace P. Nielsen},
  journal={Math. Comput.},
  year={2007},
  volume={76},
  pages={2109-2126}
}
An odd perfect number, N, is shown to have at least nine distinct prime factors. If 3 l 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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