aperture, FL, sensor size and DOF

i've noticed that sensor size makes a big difference with dof when comparing different cameras at the same aperture and focal length. what i'm wondering is what are the equivalent apertures and focal lengths for aps-c and m43 to get the same dof. for example what is the equivalent FL and F-stop in m43 for a f/4.5 83mm (35mm equiv) on aps-c?

Thanks!