SOLUTION: The sequence 2,3,5,6,7,10,... consists opf all natural numbers which are neither perfect squares nor perfect cubes. Find the 75th term of this sequence?

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Question 42841: The sequence 2,3,5,6,7,10,... consists opf all natural numbers which are neither perfect squares nor perfect cubes. Find the 75th term of this sequence?
Answer by fractalier(2101) (Show Source):
You can put this solution on YOUR website!
There is no canned method to find this except for just laying out the numbers and crossing out the squares and cubes which are
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc.
and
1, 8, 27, 64, 125, 216, etc.
So if we write out the first hundred natural numbers, it's too many because we've only crossed out 12...
Thus write out the first 90...we'd cross out 11...leaving 79 of them...thus it appears 86 is your number...as we'd cross out the same 11...leaving 75 numbers in your list...