On the asymptotic behavior of large prime factors of integers

Krishnaswami Alladi and Paul Erdős

Vol. 82 (1979), No. 2, 295–315

DOI: 10.2140/pjm.1979.82.295

Abstract

We prove results on the asymptotic behavior of Iarge prime factors of the integers. The basic idea of the paper is that if k is any fixed integer, then the k-th largest prime factor of n, denoted by P_k(n) is generally much bigger than ∑ _j>kP_j(n). We give precise estimates of this phenomenon. This paper is a sequel to an earlier paper by the authors.

Mathematical Subject Classification

Primary: 10H15, 10H15

Milestones

Received: 3 April 1978

Revised: 16 October 1978

Published: 1 June 1979