# Positive integers divisible by the product of their nonzero digits

### Florian Luca

UNAM, Campus Morelia, Michoacán, Mexico### Jean-Marie De Koninck

Université Laval, Quebec, Canada

## Abstract

Let ${\cal N}_0(x)$ denote the set of positive integers $n\le x$ which are divisible by the product of their nonzero digits. In this note, we show that if $x$ is large, then $x^{.495}<\#{\cal N}_0(x)<x^{.654}$.

## Cite this article

Florian Luca, Jean-Marie De Koninck, Positive integers divisible by the product of their nonzero digits. Port. Math. 64 (2007), no. 1, pp. 75–85

DOI 10.4171/PM/1777