The sequence 2, 3, 5, 6, 7, 10, 11, $\ldots$ contains all the positive integers from least to greatest that are neither squares nor cubes. what is the $400^{\mathrm{th}}$ term of the sequence?

The 400th term is 425.

There are floor(√400) = 20 squares in the range 1..400, so the 400th term will be at least 420. There are floor(∛420) = 7 cubes in the range 1..400, so the 400th term may be as high as 427. However, there are numbers that are both squares and cubes. Consequently, the 400th term will be 427-2 = 425.