Nicolaas Govert de Bruijn, the enchanter of friable integers

TL;DR

This paper reviews N.G. de Bruijn's foundational work on integers with small prime factors, the Dickman-de Bruijn function, and subsequent improvements, highlighting his contributions to number theory and related methods.

Contribution

It summarizes de Bruijn's original methods and recent advancements in understanding friable integers and the Dickman-de Bruijn function.

Findings

De Bruijn developed key techniques for analyzing integers with small prime factors.

The Dickman-de Bruijn function accurately models the density of friable integers.

Later work has refined and extended de Bruijn's original results.

Abstract

N.G. de Bruijn carried out fundamental work on integers having only small prime factors and the Dickman-de Bruijn function that arises on computing the density of those integers. In this he used his earlier work on linear functionals and differential-difference equations. We review the relevant work and also some later improvements by others.