In mathematics, a perfect power is any number which is some positive integer to the power of some other positive integer, excluding one of course. This includes all integer squares, cubes, fourth powers, etcetera. Some examples of perfect powers and their prime factorization:

As the second example illustrates the prime factorization will not always have the same exponent on each prime but the exponents will have at least one common factor. The On-Line Encyclopedia of Integer Sequence list for perfect powers can be found here.

IRON NODER XIV: THE RETURN OF THE IRON NODER