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Remarks on maximum and minimum exponents in factoring. (English) Zbl 0821.11004
For a positive integer \(n= p_ 1^{\alpha_ 1} \dots p_ k^{\alpha_ k}\) let \(h(n)= \min \alpha_ j\) and \(H(n)= \max \alpha_ j\). Certain distribution properties of these functions are studied and the density of integers for which \(h(n)| n\) or \(H(n)| n\) is determined.

11A25 Arithmetic functions; related numbers; inversion formulas
11B05 Density, gaps, topology
11A51 Factorization; primality
11N60 Distribution functions associated with additive and positive multiplicative functions
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