Problem 58019. Factor a number into Fermi-Dirac primes

What should be the output for numbers such as 256?
[4 64]? [16 16]?

Or 1024?
[4 256]? [4 4 64]? [4 4 4 16]? [16 64]? [4 16 16]?

Does it have to be a particular pairing(s)? If yes, how so?
Or will any/all of them work?

@Dyuman Here's my two cents:

256 = [256]. [4 64] is not valid since 64 is not a prime power where the exponent is a power of two. [16 16] is out since - I assume - you're supposed to simplify as much as possible. Same for [2 2 2 2 2 2 2 2], [4 4 4 4] and so on. But you're right that this additional requirement is needed to ensure uniqueness.

1024 = [4 256] using the same reasoning.

I added the requirement that the FD primes appear in the factorization at most once. This requirement resembles a difference between the Fermi-Dirac and the Bose-Einstein distributions of particles.