FTP, name this arithmetic function first defined by Euler, which for an integer n is the number of integers less than n that are coprime to n.
The Dirichlet series with the values of this function as coefficients evaluates to zeta of s minus one over zeta of s, while summing it over the divisors of any integer gives the integer itself. The sum of it and the sum of the divisors of an integer n is equal to 2n if and only if n is prime, and it is multiplicative for relatively prime integers. It is the order of the group of units of Z mod Z n, meaning that any unit taken to this power is one, as implied by Euler's theorem. FTP, name this arithmetic function first defined by Euler, which for an integer n is the number of integers less than n that are coprime to n.
The Dirichlet series with the values of this function as coefficients evaluates to zeta of s minus one over zeta of s, while summing it over the divisors of any integer gives the integer itself.
Euler {totient} function (or Euler {phi} function)