Grandes valeurs et nombres champions de la fonction arithmétique de Kalmár Original Research Article

The Kalmár function K(n) counts the factorizations n=x1x2…xr with xigreater-or-equal, slanted2 (1less-than-or-equals, slantiless-than-or-equals, slantr). Its Dirichlet series is image 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, image holds, while, for infinitely many nʹs, image. An integer N is called a K-champion number if M