# A generalization on the average ratio of the smallest and largest prime divisor of $n$

## TL;DR

This paper extends Erd"os and van Lint's 1982 work by estimating the average of the positive integer powers of the ratio between the smallest and largest prime divisors of integers, using C.H. Jia's method.

## Contribution

It generalizes previous results by providing estimates for higher powers of the ratio, offering a broader understanding of prime divisor distributions.

## Key findings

- Derived estimates for the average of powers of the ratio of prime divisors
- Applied C.H. Jia's method to extend previous bounds
- Enhanced understanding of prime divisor ratios in integers

## Abstract

In 1982, Erd\"os and van Lint showed an estimate for the average of the ratio of the smallest and largest prime divisor of $n$. In this note, we apply C.H. Jia's method to give an estimate for the average of positive integer power of the ratio.