MCR Bimonthly Challenge (BMC) #1 - Problem 4

The Math Contest Repository is hosting a grand festival, and they've prepared a special performance involving a group of dancers. Each dancer can perform a unique routine, and they've numbered themselves from $1$ to $1000$. The festival organizers want to showcase all possible pairs of dancers performing together in a duet.
However, there's a catch: Dancer $x$ refuses to perform with Dancer $2x$ due to a long-standing feud. How many different duets can be formed if Dancer $x$ and Dancer $2x$ never perform together?
Note that $p$ and $q$ dancing together is considered to be the same as $q$ and $p$ dancing together.