**LASZLO TOTH**

*On the asymptotic densities of certain subsets of N ^{k}*

**Pages:** 121-131

**Received:** 5 May 2001

**Mathematics Subject Classification (2000):** 11A25 - 11N37

**Abstract**:
We determine the asymptotic density d_{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}, a³≥ 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 constants d_{k} and
improve the error term
of formula (1.2) due to E. Cohen.
We point out that our treatment, based on certain
inversion functions, is applicable also in case k=1 in order to
establish asymptotic formulae with error terms regarding the densities
of subsets of **N** with
additional multiplicative properties. These generalize an often cited
result
of G. J. Rieger.

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