Propriétés multiplicatives des entiers friables translatés
An integer n is said to be y-friable if its greatest prime factor P(n) is less than y. In this paper, we study numbers of the shape n-1 when P(n) ≤ y and n ≤ x. One expects that, statistically, their multiplicative behaviour resembles that of all integers less than x. Extending a result of Basquin (2010), we estimate the mean value over shifted friable numbers of certain arithmetic functions when for some positive c, showing a change in behaviour according to whether log y/log x tends to infinity...