The distribution of $k$-free numbers

Michael J. Mossinghoff, Tomás Oliveira e Silva, Tim Trudgian

Let $R_k(x)$ denote the error incurred by approximating the number of $k$-free integers less than $x$ by $x/\zeta (k)$. It is well known that $R_k(x)=\Omega (x^{\frac{1}{2k}})$, and widely co…