Research Article

On the exponents in the factorizations of r consecutive numbers

Published in: Quaestiones Mathematicae
Volume 45 , issue 8 , 2022 , pages: 1221–1228

DOI: 10.2989/16073606.2021.1938277

Author(s): Carlo Sanna , Italy

Keywords: Primary: 11N25 , Secondary: 11N37 , 11N64 , Primary: 11N25 , Secondary: 11N37 , 11N64

Abstract

Let f (n) be the number of distinct exponents in the prime factorization of the natural number n. For every r-tuple of positive integers k = (k ₁, . . . , k _r) and for all x > 1, let be the set of natural numbers n ≤ x such that f (n+i−1) = k_i for i = 1, . . . , r. We prove that

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