In this paper we seek to generalize sigma, the sum-of-divisors function and Euler's totient function, &phis;. These functions, sigma and &phis;, are two of the most well-known arithmetic functions and have been studied extensively. Once we have defined the generalizations, we study some of the properties (in particular, growth rates, multiplicativity, and fixed points) of these generalized functions as well as their products, convolutions, and compositions. It has been noted that there is a dual nature to sigma and &phis;, and we find that this extends well to the generalized versions through the use of conjugate pairs.