Not a nanonyte - this one's a nanobug - the almost invisible one used to inject... but that's giving away part of the 'Dark Secrets' story. Nanonyteis a term invented for nano sized robots used for a variety of purposes in the A Vested Interest series of books. They first appeared in 2011, used by Liu in the second book of the series, 'Dark Secrets'.
Nanonytes can be programmed for a particular function. They self-assemble more of themselves as required, taking and adapting materials from their environment to do so. To prevent a 'grey dust' scenario where they would convert the entire world to nanonytes, there is a limit to the number of times they may replicate without further programming.
The books