2016 AIME II Problem 11

For positive integers N and k, define N to be k-nice if there exists a positive integer a such that a^{k} has exactly N positive divisors. Find the number of positive integers less than 1000 that are neither 7-nice nor 8-nice.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.