divisor function

The divisor function, often written as d(n) or σ₀(n), counts the number of positive integers that evenly divide a given number n without leaving a remainder. For example, for n=6, its divisors are 1, 2, 3, and 6, so the divisor function of 6 is 4. It helps mathematicians understand the structure and properties of numbers, especially in number theory. The function can reveal patterns and is related to things like perfect numbers and the distribution of primes. Essentially, it measures how "divisible" a number is by counting all its positive divisors.