# Arithmetic properties of positive integers with fixed digit sum

### Florian Luca

UNAM, Campus Morelia, Michoacán, Mexico

## Abstract

In this paper, we look at various arithmetic properties of the set of those positive integers $n$ whose sum of digits in a fixed base $b>1$ is a fixed positive integers $s$. For example, we prove that such integers can have many prime factors, that they are not very smooth, and that most such integers have a large prime factor dividing the value of their Euler $\phi$ function.

## Cite this article

Florian Luca, Arithmetic properties of positive integers with fixed digit sum. Rev. Mat. Iberoam. 22 (2006), no. 2, pp. 369–412

DOI 10.4171/RMI/461