Distribution Laws of Smooth Divisors

A classical result due to Deshouillers, Dress and Tenenbaum asserts that on average the distribution of the divisors of the integers follows the arcsine law. In this paper, we investigate the distribution of smooth divisors of the integers, that is, those divisors which are free of large prime factors. We show that on average these divisors are distributed according to a probability law that we will describe.