The [increasing sequence](https://artofproblemsolving.com/wiki/index.php/Increasing_sequence) $2,3,5,6,7,10,11,\ldots$ consists of all [positive integers](https://artofproblemsolving.com/wiki/index.php/Positive_integer) that are neither the [ square](https://artofproblemsolving.com/wiki/index.php/Perfect_square) nor the [ cube](https://artofproblemsolving.com/wiki/index.php/Perfect_cube) of a positive integer. Find the 500th term of this sequence.
Because there aren't that many perfect squares or cubes, let's look for the smallest perfect square greater than $500$. This happens to be $23^2=529$. Notice that there are $23$ squares and $8$ cubes less than or equal to $529$, but $1$ and $2^6$ are both squares and cubes. Thus, there are $529-23-8+2=500$ numbers in our sequence less than $529$.  Magically, we want the $500th$ term, so our answer is the biggest non-square and non-cube less than $529$, which is $\boxed{528}$.