Divisor functions are mathematical functions that count the number of divisors of a given integer. For example, the divisor function d(n) gives the total number of positive divisors of the integer n. This function is useful in number theory and has applications in various areas, including cryptography and combinatorics. Another important divisor function is the sum of divisors function, denoted as \sigma(n). This function calculates the sum of all positive divisors of n. Both d(n) and \sigma(n) help mathematicians understand the properties of numbers and their relationships, contributing to the study of prime numbers and factorization.