heh. don't hold your breath.
there is definitely NOT a simple formula for either of these sums.
as for the first one, even Leonhard Euler, the greatest mathematician of all time, could only muster a strange-looking approximation:
http://www.umass.edu/wsp/statistics/math/euler.htmlas for the second one, that's not much better. in fact, if you can produce a reliable formula for things like that, then you're well on your way to
winning a million dollars. seriously. (click the link for details)