The sequence 2, 3, 5, 6, 7, 10, 11, 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?
I'm seeing it's 425.
I don't have a suggestion on how to find that though.
I guess you could start at 400 and add 1 for every square or cube you encounter in the list
There are 20 squares <= 400, 1-20,
There are 7 cubes <= 400, 1-7
But you seem to be excluding 1 from the series and that's counted here twice so we only have 25 squares and cubes.
Thus the 400th element is 425.