J. de Koninck

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math.NT2026

The Integer Values of $\sum_{i = 1}^{n} \frac{1}{g c d ( n , i )}$

Jean-Marie De Koninck, Patrick Letendre

We study the set of integers $n \leq x$ for which $\sum_{i = 1}^{n} \frac{1}{g c d ( n , i )}$ takes an integer value. We show that the number of such integers is $≪ x^{2/3 + ε}$ for all fix…

math.NT2023

On the tower factorization of integers

Jean-Marie De Koninck, William Verreault

Under the fundamental theorem of arithmetic, any integer $n > 1$ can be uniquely written as a product of prime powers $p^{a}$ ; factoring each exponent $a$ as a product of prime powers…

math.NT2023

Arithmetic functions at factorial arguments

Jean-Marie De Koninck, William Verreault

For various arithmetic functions $f : N \to R$ , the behavior of $f (n!)$ and that of $\sum_{n \leq N} f (n!)$ can be intriguing. For instance, for some functions $f$ , w…

The Integer Values of ∑i=1n​gcd(n,i)1​

On the tower factorization of integers

Arithmetic functions at factorial arguments

The Integer Values of $\sum_{i = 1}^{n} \frac{1}{g c d ( n , i )}$