Let 2,3,5,6,7,10,11,... be an increasing sequence of positive integers that are neither the perfect squares nor the cubes. Find the 1991st term.
Let's define to be the number of numbers less than or equal to such that they are neither the perfect squares or cubes.
We then have .
The intuition behind is we take every number up to and then subtract all of the perfect squares and cubes. We must then account for any duplicates.
Now solve .