Ordered prime divisors of a random integer
type: Item
instance of: scholarly article
title: Ordered prime divisors of a random integer
zbMATH Open document ID: 0551.10042
author: Stuart P. Lloyd
published in: The Annals of Probability
publication date: 1984-01-01T00:00:00Z
review text: The author attempts to find the harmonic density of integers \(n\leq N\) whose r-th largest prime divisor does not exceed \(N^ x\), \(0\leq x\leq 1\). Ignoring that densities (harmonic or natural) are additive but not \(\sigma\)-additive, the author works on an abstract probability space in which prime divisors are independent, and from limit theorems in such a large (abstract) space the conclusion is drawn that the harmonic density of the above set exists, and these densities are identified. The result, however, may or may not have anything to do with densities in view of the oversight mentioned earlier.
Mathematics Subject Classification ID: 11K99
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11N05
zbMATH DE Number: 3877297
zbMATH Keywords: large prime divisors
zbMATH Keywords: harmonic density of integers
reviewed by: Janos Galambos
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993149
OpenAlex ID: W2066124265
DOI: 10.1214/AOP/1176993149
description: scientific article; zbMATH DE number 3877297