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Odd perfect numbers have at least nine distinct prime factors

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byPace P. Nielsen;

Math. Comp. 76 (2007), 2109-2126

DOI: https://doi.org/10.1090/S0025-5718-07-01990-4

Published electronically: May 9, 2007

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Abstract:

An odd perfect number, NNN, is shown to have at least nine distinct prime factors. If 3nmidN3\nmid N3nmidN then NNN must have at least twelve distinct prime divisors. The proof ultimately avoids previous computational results for odd perfect numbers.

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