On some properties of divisor function

Abstract

Recall that the divisor function d(n) counts the number of positive divisors of n. For instance, d (1) = 1, d (2) = d (3) = 2, d (4) = 3, and so on. In this work, we present the most important properties of the divisor function d (n). By design, some of the properties require to use several multiplicative functions. For future research there are several types of open questions related to the divisor function as well as Diophantine equations and inequalities.