I'm using an audio amplifier to produce a 15-20 kHz, 6 watt sine wave output into a pure resistive load. There are some low-frequency components to this signal that I want to remove (mains frequency harmonics). How is this best achieved? I know how to construct RC filters for signal (i.e. low) voltage circuits but not power circuits. Can someone give an answer about how I should design the filter and suggest components that may work?
You could do what they do in speakers : -
In other words use capacitors and inductors to control the frequencies that are most directed to the tweeter. There are plenty of articles on-line about this. Try searching "speaker crossover circuit".
Or you can do a similar thing with the signal before it goes into the amplifier. The signal powers are much smaller and it will be cheaper to use smaller components.
How is this best achieved?
It's a bit like asking what the best car is. So, state what you want to achieve spectrally and design a high-pass filter to suit. Maybe something like this that uses an RLC: -
I've chosen values of 1000 uH, 1 uF and 40 ohms to give a fairly flat response from 6 kHz and above. You could also use an active sallen key low pass filter but now it's possible getting more complex.
However, if you want a really steep decline in those frequencies rejected below 6 kHz then multiple 2nd order filters might be needed.