A divisor function is a mathematical function that counts the number of divisors of a given integer. For example, if you take the number 12, its divisors are 1, 2, 3, 4, 6, and 12, so the divisor function for 12 would return 6. This function is often denoted as d(n) or \sigma_0(n) , where n is the integer in question. Divisor functions are important in number theory and have applications in various areas, including algebra and combinatorics. They help in understanding the properties of numbers, such as their factorization and relationships with prime numbers. Additionally, divisor functions can be used in more complex functions, like the Riemann zeta function, which connects to the distribution of prime numbers.