Grandes valeurs et nombres champions de la fonction arithmétique de Kalmár

The Kalmár function K(n) counts the factorizations n=x1x2…xr with xi⩾2 (1⩽i⩽r). Its Dirichlet series is where ζ(s) denotes the Riemann ζ function. Let ρ=1.728… be the root greater than 1 of the equation ζ(s)=2. Improving on preceding results of Kalmár, Hille, Erdős, Evans, and Klazar and Luca, we show that there exist two constants C5 and C6 such that, for all n, holds, while, for infinitely many n's, .An integer N is called a K-champion number if M