The intermediate prime divisors of integers
Open Access
- 1 January 1987
- journal article
- research article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 101 (2) , 213-216
- https://doi.org/10.1090/s0002-9939-1987-0902529-x
Abstract
Let p 1 > p 2 > ⋯ > p ω {p_1} > {p_2} > \cdots > {p_\omega } be the distinct prime divisors of the integer n n . If ω = ω ( n ) → + ∞ \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 ω − j \omega - j tend to infinity with n n . We show that log log 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.This publication has 4 references indexed in Scilit:
- Probabilistic Number Theory IIPublished by Springer Nature ,1980
- Probabilistic Number Theory IPublished by Springer Nature ,1979
- The sequences of prime divisors of integersActa Arithmetica, 1976
- Remarks on the Poisson processPublished by Springer Nature ,1967