The divisor function, often denoted as d(n) , counts the number of positive divisors of a given integer n . For example, if n = 12 , the positive divisors are 1, 2, 3, 4, 6, and 12, so d(12) = 6 . This function is important in number theory and has applications in various mathematical fields. Another related function is the sum of divisors, denoted as \sigma(n) , which adds up all the positive divisors of n . For instance, \sigma(12) = 1 + 2 + 3 + 4 + 6 + 12 = 28 . Both the divisor function and the sum of divisors are studied in the context of prime factorization and multiplicative functions.