The least common multiple of all $mn$ can be written as $K=2^{20}p$ where $p$ is odd. This is because $2017 > 1024 = 2^{10}$. Then, when all the terms are written in denominator $K$, all the numerators are even except the term derived from $\frac{1}{1024\times 1024}$. This means the sum of all numerators is odd. However, the denominator is even. Hence, it cannot be an integer.