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The intermediate prime divisors of integers


Authors: J.-M. De Koninck and J. Galambos
Journal: Proc. Amer. Math. Soc. 101 (1987), 213-216
MSC: Primary 11K99
MathSciNet review: 902529
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Abstract: Let $ {p_1} < {p_2} < \cdots < {p_\omega }$ be the distinct prime divisors of the integer $ n$. If $ \omega = \omega (n) \to + \infty $ with $ n$, then $ {p_j}$ is called an intermediate prime divisor of $ n$ if both $ j$ and $ \omega - j$ tend to infinity with $ n$. We show that $ \log \log {p_j}$, as $ j$ goes through the indices for which $ {p_j}$ is intermediate, forms a limiting Poisson process in the sense of natural density.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0902529-X
Article copyright: © Copyright 1987 American Mathematical Society