You're right - I don't know what I was thinking.

If n is a perfect square, then log(N(n)) = log(1) = 0, so that power(n) is undefined. Otherwise, if n is powerful, it would seem that each prime in the prime factorization of n would add at least 3 times the value to the numerator as the denominator, so that power(n) is greater than or equal to 3.

- Hollywood