Abstract

Let p 1 > p 2 > ā‹Æ > p Ļ‰ {p_1} > {p_2} > \cdots > {p_\omega } be the distinct prime divisors of the integer n n . If Ļ‰ = Ļ‰ ( n ) ā†’ + āˆž \omega = \omega (n) \to + \infty with n n , then p j {p_j} is called an intermediate prime divisor of n n if both j j and Ļ‰ āˆ’ j \omega - j tend to infinity with n n . We show that log ā” log ā” p j \log \log {p_j} , as j j goes through the indices for which p j {p_j} is intermediate, forms a limiting Poisson process in the sense of natural density.

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