Number theoretic functions are mathematical functions that take integers as inputs and produce integers as outputs. These functions often reveal important properties of numbers, such as their divisibility, prime factors, and relationships to other numbers. Common examples include the Euler's totient function, which counts the integers up to a given integer that are coprime to it, and the divisor function, which counts the number of divisors of an integer. These functions play a crucial role in various areas of mathematics, particularly in number theory, which studies the properties and relationships of integers. They are also essential in applications like cryptography, where understanding the structure of numbers can enhance security protocols.