Papers by Jean-Marie De Koninck
Publicationes Mathematicae Debrecen
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Archivum Mathematicum, 2020
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Colloquium Mathematicum, 2020
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Mathematica Slovaca, 2018
Given an additive function f and a multiplicative function g, let E(f, g;x) = #{n ≤ x: f(n) = g(n... more Given an additive function f and a multiplicative function g, let E(f, g;x) = #{n ≤ x: f(n) = g(n)}. We study the size of E(ω,g;x) and E(Ω,g;x), where ω(n) stands for the number of distinct prime factors of n and Ω(n) stands for the number of prime factors of n counting multiplicity. In particular, we show that E(ω,g;x) and E(Ω,g;x) are $\begin{array}{} \displaystyle O\left(\frac{x}{\sqrt{\log\log x}}\right) \end{array}$ for any integer valued multiplicative function g. This improves an earlier result of De Koninck, Doyon and Letendre.
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Canadian Mathematical Bulletin, 2018
Let $k$ be an arbitrary positive integer and let $\unicode[STIX]{x1D6FE}(n)$ stand for the produc... more Let $k$ be an arbitrary positive integer and let $\unicode[STIX]{x1D6FE}(n)$ stand for the product of the distinct prime factors of $n$. For each integer $n\geqslant 2$, let $a_{n}$ and $b_{n}$ stand respectively for the maximum and the minimum of the $k$ integers $\unicode[STIX]{x1D6FE}(n+1),\unicode[STIX]{x1D6FE}(n+2),\ldots ,\unicode[STIX]{x1D6FE}(n+k)$. We show that $\liminf _{n\rightarrow \infty }a_{n}/b_{n}=1$. We also prove that the same result holds in the case of the Euler function and the sum of the divisors function, as well as the functions $\unicode[STIX]{x1D714}(n)$ and $\unicode[STIX]{x1D6FA}(n)$, which stand respectively for the number of distinct prime factors of $n$ and the total number of prime factors of $n$ counting their multiplicity.
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Acta Arithmetica, 1995
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Annales mathématiques du Québec, 2017
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Uniform distribution theory, 2016
We introduce the concept of strong normality by defining strong normal numbers and provide variou... more We introduce the concept of strong normality by defining strong normal numbers and provide various properties of these numbers, including the fact that almost all real numbers are strongly normal.
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Acta Cybernetica, 2015
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Publications Mathématiques de Besançon, 2015
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A positive integer is said to be a Niven number if it is divisible by the sum of its decimal digi... more A positive integer is said to be a Niven number if it is divisible by the sum of its decimal digits. We investigate the occurrence of large and small gaps between consecutive Niven numbers.
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Functiones et Approximatio Commentarii Mathematici, 2015
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Colloquium Mathematicum, 2014
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Journal of the Australian Mathematical Society, 2009
Given an integer n≥2, let λ(n):=(log n)/(log γ(n)), where γ(n)=∏ p∣np, denote the index of compos... more Given an integer n≥2, let λ(n):=(log n)/(log γ(n)), where γ(n)=∏ p∣np, denote the index of composition of n, with λ(1)=1. Letting ϕ and σ stand for the Euler function and the sum of divisors function, we show that both λ(ϕ(n)) and λ(σ(n)) have normal order 1 and mean value 1. Given an arbitrary integer k≥2, we then study the size of min {λ(ϕ(n)),λ(ϕ(n+1)),…,λ(ϕ(n+k−1))} and of min {λ(σ(n)),λ(σ(n+1)),…,λ(σ(n+k−1))} as n becomes large.
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Functiones et Approximatio Commentarii Mathematici, 2011
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Papers by Jean-Marie De Koninck