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