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D. E. Iannucci and R. M. Sorli, "On the total number of prime factors of an odd perfect number," Math. Comp., 72:244, (2003) 2077--2084.  MR 1986824
Abstract: We say nN is perfect if σ(n)=2n, where σ(n) denotes the sum of the positive divisors of n. No odd perfect numbers are known, but it is well known that if such a number exists, it must have prime factorization of the form n=pαj=1kqjj, where p, q1, ..., qk are distinct primes and p≡α≡1 (mod 4) . We prove that if βj≡1 (mod 3) or βj≡2 (mod 5) for all j, 1≤ j k, then 3does not divide n. We also prove as our main result that Ω(n)≥37, where Ω(n)=α+2∑j=1kβj. This improves a result of Sayers (Ω(n)≥ 29) given in 1986.
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