A perfect power is a number that can be written as a positive integer raised to an integer power greater than $1$. For example, $125$ is a perfect power because it is equal $5^3$. The list $2$, $3$, $5$, $6$, $7$, $10$, $11$, $12$, $13$, $14$, $15$, $17$, $\cdots$ contains every positive integer less than $1000$ that is not a perfect power. How many integer are in the list?