On natural densities of sets of some type integers

Dmitry I. Khomovsky

Let $a_0=b_0=0$ and $0<a_1\le b_1<a_2\le b_2<\dots \le b_n$ be integers. Let $Q\left(x;{\bigcup }_{j=1}^n[a_j,b_j]\right)$ be the number of integers between $1$ and $x$ such th…