In number theory, the totient f(n) of a positive integer n is defined to be the number of positive integers less than or equal to n that are coprime to n (i.e. having no common positive factors other than 1).
In particular f(1)=1 since 1 is coprime to itself (1 being the only natural number with this property).
For example, f(9)=6 since the six numbers 1, 2, 4, 5, 7 and 8 are coprime to 9.
The function f(n) so defined is the totient function.
The totient is usually called the Euler totient or Euler's totient, after the Swiss mathematician Leonhard Euler, who studied it.
