Odd perfect numbers have at least nine distinct prime factors

Nielsen, Pace

doi:10.1090/S0025-5718-07-01990-4

Odd perfect numbers have at least nine distinct prime factors
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Math. Comp. 76 (2007), 2109-2126 Request permission

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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