Squares: there are 44 of them (44*44=1936 but 45*45=2025)
Cubes: there are 12 of them (up to 12*12*12=1728) but exclude 1^3, 4^3, and 9^3 as those are also squares, so just 9 unique ones.
Fourth powers (and all non-prime powers)—are included under lower-ranked exponents
Fifth powers: 4 of them (up to 4*4*4*4*4=1024, but exclude 1^5 and 4^5 as they are also squares, so just 2 unique ones
Seventh powers: Just 1 unique one: 2^7=128.
Once we get up to 11th powers or higher, the lowest unique example is 2^11=2048 which is too big.
So in total, there are 44+9+2+1=56 such numbers up to 2000.
