Affiliation:
1. Faculty of Information Technology and Business, Cyber University, 7F Shibakoen Front Tower, 2-6-3 Shibakoen Minato-ku, Tokyo 105-8011, Japan
Abstract
Let [Formula: see text] be a fixed positive number. Define [Formula: see text] as the number of positive integers [Formula: see text] having no prime factors [Formula: see text], and define [Formula: see text] as the number of positive integers [Formula: see text] having [Formula: see text] prime factors [Formula: see text], with all the other prime factors [Formula: see text]. In this paper, we give an asymptotic estimate for the ratio [Formula: see text], provided that [Formula: see text], [Formula: see text], and [Formula: see text] as [Formula: see text]. Also, combining this estimate with conventional ones for [Formula: see text], we provide sharp estimates for [Formula: see text].
Publisher
World Scientific Pub Co Pte Ltd
Subject
Algebra and Number Theory