If there are exactly two groups (up to isomorphism) of order $n$, then $n$ is the product of two primes.
This isn't if and only if, it doesn't capture "distinct", and it doesn't cover "prime powers", but at least it's nontrivial.
If there are exactly two groups (up to isomorphism) of order $n$, then $n$ is the product of two primes.
This isn't if and only if, it doesn't capture "distinct", and it doesn't cover "prime powers", but at least it's nontrivial.