Union of Prime Numbers & Non-Powers of Integers: Usage & Contexts

[Swamp Thing]

Is there a name for the union of {prime numbers} and {integers that are not powers of integers}?

For example, we would include 2, 3, 5, 7, 11... And also 6, 10, 12...

But we exclude 2^n, 3^n, ... and 6^n , 10^n , etc.

What are some interesting contexts where this set crops up?

 

[Swamp Thing]

A rather silly question, I now realize : The first set is a subset of the second one anyway. And they are just "not perfect powers".