Among the first 2009 numbers, there are () numbers that are neither square nor cubic

Among the first 2009 numbers, there are () numbers that are neither square nor cubic

What is the square number
1^2,2^2.44^2
A total of 44
Cubic number
1^3.2^3,.12^3
12 in total
Repetitive
1,64,729
So there are a total of 2009-44-12 + 3 = 1956

How many of the first 2008 are neither square nor cubic

44*44=1936< 2008 45*45=2025>2008
So there are 44 squares
12^3=17282008
So there are 12 squares
Consider the number satisfying x ^ 2 = y ^ 3, which must be the sixth power of a certain number
3^6=7292008
That is, 1 ^ 2 = 1 ^ 3 8 ^ 2 = 4 ^ 3 27 ^ 2 = 9 ^ 3
Remove the number of these three repetitions
The number of squares or cubes is 44 + 12-3 = 53
The first 2008 numbers that are neither square nor cubic are 2008-53 = 1955

In the first 2001 positive integers, there are several that are neither square nor cubic

2001-44 (square) - 12 (cubic) + 2 (4 * 4 * 4,9 * 9 * 9 is both square and cubic) = 1947