One way of computing it is through the Mobius inversion formula, and when applied to a perfect square, it is equal to the square root of the argument times it applied to the square root. It can give the degree of a cyclotomic extension over the rational numbers and the prime number theorem sets bounds on its growth. In the 
One way of computing it is through the Mobius inversion formula, and when applied to a perfect square, it is equal to the square root of the argument times it applied to the square root. It can give the degree of a cyclotomic extension over the rational numbers and the prime number theorem sets bounds on its growth. In the generalized version of Fermat's Little Theorem, this function of n appears in the exponent of an integer relatively prime to n, and if the Goldbach conjecture is true, for every number m, there exist two prime numbers such that the sum of this function applied to each of them gives 2m. Equivalent to the number of elements in the ring of units of Z sub n, FTP, identify this function which gives the number of integers relatively prime to its argument.
One way of computing it is through the Mobius inversion formula, and when applied to a perfect square, it is equal to the square root of the argument times it applied to the square root.
Euler phi function (or totient function)