On the number of prime factors of an odd perfect number
نویسندگان
چکیده
Let Ω(n) and ω(n) denote respectively the total number of prime factors and the number of distinct prime factors of the integer n. Euler proved that an odd perfect number N is of the form N = pem2 where p ≡ e ≡ 1 (mod 4), p is prime, and p ∤ m. This implies that Ω(N) ≥ 2ω(N) − 1. We prove that Ω(N) ≥ (18ω(N) − 31)/7 and Ω(N) ≥ 2ω(N) + 51.
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ورودعنوان ژورنال:
- Math. Comput.
دوره 83 شماره
صفحات -
تاریخ انتشار 2014