HMMT November 2013 U34

Find the number of positive integers less than 1000000 that are divisible by some perfect cube greater than 1. Your score will be $\max \left\{0,\left\lfloor 20-200\left|1-\frac{k}{S}\right|\right\rfloor\right\}$, where $k$ is your answer and $S$ is the actual answer.