Does Mars have the gravitational wherewithal to support a breathable atmosphere?

I know that the current one is little better than hard vacuum. I suspect (not having taken any physics) that since its mass is ⅓ of Earth’s, and its gravity ⅓ g, its greatest amount of air pressure would only be about 253mmHg at what amounts to Martian sea level.

Surely there’s more precise data that my guesses.