What are the two factors that most greatly influence whether a planet can sustain a dense atmosphere ?

The answer is;

The bigger the planet, the greater its gravitational force. Therefore, bigger planets tend to have  a thicker atmosphere.  

The further away the planet is from its star, the higher the likelihood that it can keep a dense atmosphere. This is because planet close to the star like the sun tend to have the molecules of the atmosphere highly energized (due to high bombardment by photons) that they can escape the planet’s gravitation pull and escape into space.  

this is math not biology xd