On the asymptotic densities of certain subsets of \(\mathbb N^k\) (Q2777996)
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scientific article; zbMATH DE number 1719313
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the asymptotic densities of certain subsets of \(\mathbb N^k\) |
scientific article; zbMATH DE number 1719313 |
Statements
6 March 2003
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arithmetical functions
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asymptotic density of sets
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On the asymptotic densities of certain subsets of \(\mathbb N^k\) (English)
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Let \(k\geq 2\) be a fixed integer and \(D_k\) the set of \(k\)-tuples \((n_1,n_2,\dots, n_k)\in \mathbb{N}^k\), such that no prime power \(p^a\), \(a\geq 1\), appears in the canonical factorization of each \(n_i\), \(1\leq i\leq k\). The author determines the asymptotic density \(\delta_k\) of \(D_k\), gives some numerical values and deduces asymptotic formulae with error terms regarding this and related problems. This generalizes results of E. Cohen and G. J. Rieger.
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