In Swedish, the term "stordator", literally "big computer" refers to a mainframe.
I really like your idea of nano and picocomputers. It's consistent, and really reflects on the miniaturisation that we have seen since since the invention of the computer.
Since "computer" pre-dates digital, it might be a good time to come up with a more apt base term too. It's not as if most people's usage of them (at least as far as they know!) is performing arithmetic.