Do let me know how you get on, I'd like to find ways to simplify it to maximise its accessibility - I've tried to do so already, but I've been playing with many of these concepts for over 25 years, so it's not always easy to recognise when what seems obvious to me would not be so to someone else.
One of the particularly appealing aspects of number theory is how far you can go with nothing but basic arithmetic and some simple algebra - if it were competently explained, I think a (motivated) O-level student should be able to understand the whole thing.
What is difficult to explain, and probably impossible to teach, is looking at a single example and saying "hey, that's a pattern", or looking at that 43 and thinking "I don't know how it'd help, but that should really be a 42" - as far as I know, that's the intuition that develops from toying with this sort of thing on a regular basis over an extended period.
I had intended to add some links to the Mathworld definitions, but forgot. I'll go back and do that.