Sur une proposition empirique énoncée au Bulletin
Sur une somme liée à la fonction de Möbius.
Sylvester: ushering in the modern era of research on odd perfect numbers.
Tau numbers: a partial proof of a conjecture and other results.
The average order of the Dirichlet series of the gcd-sum function.
The composition of the gcd and certain arithmetic functions.
The distribution of Farey numbers.
The distribution of totients.
The divisor function on residue classes I
The Fourier transform of functions of the greatest common divisor.
The general quasi-order algorithm in number theory.
The Generation of Arithmetical Identities.
The number of relatively prime subsets and phi functions for .
The number of relatively prime subsets of .
The number of restricted solutions of some systems of linear congruences
The number of solutions of .
The range of the sum-of-proper-divisors function
Answering a question of Erdős, we show that a positive proportion of even numbers are in the form s(n), where s(n) = σ(n) - n, the sum of proper divisors of n.
The ring of arithmetical functions with unitary convolution: Divisorial and topological properties
We study , the ring of arithmetical functions with unitary convolution, giving an isomorphism between and a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett [NumThe] between the ring of arithmetical functions with Dirichlet convolution and the power series ring on countably many variables. We topologize it with respect to a natural norm, and show that all ideals are quasi-finite. Some elementary results on factorization into atoms...
The unitary amicable pairs to .
The unitary analogue of Pillai's arithmetical function.