Arithmetic subderivatives and Leibniz-additive functions

We introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative and arithmetic partial derivative. In order to generalize these notions a step further, we define that an arithmetic function is Leibniz-additive if there is a nonzero-valued and completely multiplicative function ℎ satisfying () = ()ℎ () + ()ℎ () for all positive integers and . We study some basic properties of such functions. For example, we present conditions when an arithmetic function is Leibniz-additive and, generalizing the well-known bounds for the arithmetic derivative, we establish bounds for a Leibniz-additive function.Validerad;2020;Nivå 2;2020-01-31 (johcin)