Integers without large prime factors: from Ramanujan to de Bruijn

TL;DR

This paper surveys historical progress on estimating integers lacking large prime factors, highlighting de Bruijn's pivotal 1950 results that significantly advanced the field and marked a new era of research.

Contribution

It provides a concise overview of the development of methods for counting integers without large prime factors, emphasizing de Bruijn's influential contributions.

Findings

De Bruijn's 1950 results revolutionized the field.

Historical survey of key developments up to 1950.

Significant progress in estimating integers without large prime factors.

Abstract

A small survey of work done on estimating the number of integers without large prime factors up to around 1950 is provided. Around 1950 N.G. de Bruijn published results that dramatically advanced the subject and started a new era in this topic.