Definitions of sets How would I define the set $\Omega_2(x)\ =\ \{4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39\dots\}$, where $\Omega_2$ is the set of semi primes (ie - numbers with $2$ not necessarily distinct prime factors)? I would like to define $\Omega_3$, etc. in a similar way.
I was thinking something along the lines of $\Omega_2(x)\ :=\{\mathbb{P}_p\cdot \mathbb{P}_q\ \rm{s.t}\ p=q\  \vee p \neq q \} $
Update
$\Omega_2 \in \mathbb{N}\ \text{s.t.}\ \Omega_2:=\{\mathbb{P}_p\cdot \mathbb{P}_q\ \rm{s.t.}\ p=q\  \vee p \neq q \}\text{ where } p \wedge q \in \mathbb{N}$

$$\Omega_k = \underbrace {\mathbb{P}\cdot\mathbb{P}\cdots\mathbb{P}}_{\text{k times}}$$
Here $\mathbb{P}$ is a set of primes and $A \cdot B = \{a \cdot b \mid a \in A, b \in B \}$.
