Resumen de Arithmetic properties of positive integers with fixed digit sum

Florian Luca

• 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 integer 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 f function.