On composite n for which φ(n) | n -1
On consecutive Farey arcs
On consecutive Farey arcs II
On consecutive integers divisible by the number of their divisors
We prove that there are no strings of three consecutive integers each divisible by the number of its divisors, and we give an estimate for the number of positive integers n ≤ x such that each of n and n + 1 is a multiple of the number of its divisors.
On Consecutive k'th Power Residues.
On cubic polynomials giving many primes.
On differences of two squares
The arithmetic function ρ(n) counts the number of ways to write a positive integer n as a difference of two squares. Its average size is described by the Dirichlet summatory function Σn≤x ρ(n), and in particular by the error term R(x) in the corresponding asymptotics. This article provides a sharp lower bound as well as two mean-square results for R(x), which illustrates the close connection between ρ(n) and the number-of-divisors function d(n).
On Dirichlet characters of polynomials
On Dirichlet convolution method.
On distribution of arithmetical functions on the set prime plus one
On distribution of values of σ(n) in residue classes
On Divisor Problems in Connection with Squarefree Numbers.
On divisors of sums of integers. II.
On divisors whose sum is a square
On Euler-von Mangoldt's equation
On exponential sums involving the divisor function.
On exponential sums with multiplicative coefficients, II
On Exponents in Arithmetical Semigroups.
On extremal sets without coprimes
On -thin sets