Solution:
Consider numbers which are Squares,cubes, fourths, fifths of some natural numbers.
For example, Starting from squares of some natural number: 4,9,16,25,36,49,64......
and their factors , which are 4= 1 × 2×1×2
9=1×3×1×3
16=2×1×2×1×2×1×2×1
25=1×5×1×5
36=2×3×2×3
64=2×4×2×4
Now coming to cubic numbers
8= 1 ×2×1×2×1×2
27= 1×3×1×3×1×3
3125= 3 ×5×3×5×3×5
So,the numbers whose factor pairs repeats are square, cubic, fourth,Fifth ,Sixth and.....higher powers of natural Numbers.
→→→So, we just need to check that whether those numbers whose factor pairs repeats are Squares, cubes or higher powers of natural numbers.