Need help with project

I need to generate a simple data list of sorting out a certain type of number from any specified range of integers.

Example: range 8 through 16. I want to only keep primes and composites made up any power of two multiple of a prime (12 is a good example of p * 2^n because 12=3*2^2). So, for example, from range 8 through 16, I would need to sort and store 8,10,11,12,13,14,16. 9 and 15 are neither prime, nor a 2^n multiple of a prime, so they are excluded. As I said, I'd like to specify any range such as 16-32, 100-500, and so on. I might want to put a ceiling of some sort so you can overload the computer.