19 research outputs found
Odd Perfect Numbers Have At Least Nine Distinct Prime Factors
An odd perfect number, N, is shown to have at least nine distinct prime
factors. If 3 does not divide N, then N must have at least twelve distinct
prime divisors. The proof ultimately avoids previous computational results for
odd perfect numbers.Comment: 17 page
The Abundancy Index of Divisors of Odd Perfect Numbers
If is an odd perfect number, where is the Euler prime,
then we show that is sufficient for Sorli's conjecture that to hold. We also prove that , and that , where is the abundancy index of .Comment: 10 page