[Noob warning]: I am not a mathematician. If you use jargon, please explain or reference.
Other than $f(x)=x!$, what is a univariate non-piecewise function with a domain that is either all integers, or an infinite-sized subset of all integers, and whose range contains only integers and exactly one prime number?
For those that prefer lists, here are the criteria again:
- Univariate (one independent variable)
- Not $f(x)=x!$ (of which I 'think' meets the criteria below...)
- Non-piecewise (non-hybrid)
- Domain is either all integers or an infinite-sized subset of all integers
- Range contains only integers
- Range contains exactly one prime number