Problems involving the relation of one number-theoretic function to some manipulation of another are also an interest of mine. These proofs tend to allow for more creativity. Instead of defining a function, F(n), and another, G(n), and demonstrating them to be equal, we take a more abstract approach. We define a function, F(n), which is some manipulation of a single or many number-theoretic functions (typically a sum for divisors of n) and show that F represents some quality. We then establish that another number-theoretic function, G(n), represents the same quality. In doing so, we've formulated G(n) as F(n).