Problem #WSP-000348

Problem

A robot is programmed to move along the number line starting at $2$. At each second, the number by which it moves up by must be a factor of the number it’s currently on, but not $1$. For example, if the robot gets to $10$, then it can move forward by $2$, $5$ or $10$ steps, going to $12$, $15$, or $20$. What numbers can it land on, and what numbers can’t it land on?