Euler's totient function, also known as Euler's phi function, is a mathematical function that counts the number of positive integers less than or equal to a given number that are relatively prime to that number.
The notation used for Euler's totient function is φ(n), where n is the given number.
Euler's totient function can be calculated using the formula φ(n) = n * (1-1/p1) * (1-1/p2) * ... * (1-1/pk), where p1, p2, ..., pk are the distinct prime factors of n.
Euler's totient function has many applications in number theory and cryptography. It is also used in the RSA encryption algorithm.
The Carmichael function is a generalization of Euler's totient function. While Euler's totient function counts the number of integers relatively prime to a given number, the Carmichael function counts the number of integers with a given residue modulo n. The Carmichael function is always less than or equal to Euler's totient function.