Larry's advice is very good, see if you can put it on another circuit, that would be your cheapest fix. If not, a dedicated line would be your second cheapest option. If you cannot do that, you could try buying a power conditioner that uses isolation transformers, like Equi=Tech.
What power conditioner will help in my situation?
The only power outlets I have are on the same circuit as the ceiling fan. When I change the fan speed there is a low frequency hum when I turn the fan speed from low to medium etc.
Aside from running a dedicated line, will a power regenerator or conditioner eliminate this?
Aside from running a dedicated line, will a power regenerator or conditioner eliminate this?