I've come across a way to generalize the Mobius function, and found that there's already so-called Mobius generalized functions (Apostol, 1970?, etc.)
However, my generalization is different from Apostol's it seems, plus it allows me to write $\zeta(s)^{-k}$ as a function of it, and I also can give a power series for it.
I am writing a paper on NT, which I hope to publish after I'm done typing it, and just want to make sure what is new and what is not.