On Squarefree Numbers in Arithmetic Progressions.
On sums involving reciprocals of the largest prime factor of an integer II
On the asymptotic behavior of the Dickman-de Bruijn function.
On the asymptotic formulas for powerful numbers.
On the Barban-Davenport-Halberstam theorem: IX
On the Barban-Davenport-Halberstam theorem: XI
On the congruence .
On the densities of sets of multiples.
On the diameter of sets of almost powers
On the difference of consecutive terms of sequences defined by divisibility properties
On the distribution of consecutive square-free primitive roots modulo
A positive integer is called a square-free number if it is not divisible by a perfect square except . Let be an odd prime. For with , the smallest positive integer such that is called the exponent of modulo . If the exponent of modulo is , then is called a primitive root mod . Let be the characteristic function of the square-free primitive roots modulo . In this paper we study the distribution and give an asymptotic formula by using properties of character sums.
On the distribution of integers with a fixed number of prime factors.
On the Distribution of M-tuples of B-numbers
On the distribution of natural numbers with divisors from an arithmetic progression
On the Distribution of Prime Divisors of n
On the distribution of some integers related to perfect and amicable numbers
On the Distribution of Square-Full and Cube-Full Integers.
On the Distribution of Square-full and Cube-full Numbers.
On the distribution of subsets of primes in the prime factorization of integers
On the distribution of the Euler function of shifted smooth numbers
We give asymptotic formulas for some average values of the Euler function on shifted smooth numbers. The result is based on various estimates on the distribution of smooth numbers in arithmetic progressions which are due to A. Granville and É. Fouvry & G. Tenenbaum.