1 9 O ct 2 00 6 On the asymptotic densities of certain subsets of N k László Tóth


We determine the asymptotic density δ k of the set of ordered k-tuples (n 1 , ..., n k) ∈ N k , k ≥ 2, such that there exists no prime power p a , a ≥ 1, appearing in the canonical factorization of each n i , 1 ≤ i ≤ k, and deduce asymptotic formulae with error terms regarding this problem and analogous ones. We give numerical approximations of the… (More)