Definition:Euler Phi Function

Definition
Let $n \in \Z_{>0}$, that is, a strictly positive integer.

The Euler $\phi$ (phi) function is the arithmetic function $\phi: \Z_{>0} \to \Z_{>0}$ defined as:


 * $\map \phi n = $ the number of strictly positive integers less than or equal to $n$ which are prime to $n$

That is:
 * $\map \phi n = \card {S_n}: S_n = \set {k: 1 \le k \le n, k \perp n}$

Also known as
The Euler $\phi$ function is also known as the totient function or the indicator function

Some sources render it with a hyphen: Euler $\phi$-function.

Some sources merely refer to it as Euler's function.

Also see

 * Euler Phi Function of 1: $\map \phi 1 = 1$


 * Definition:Cototient
 * Definition:Noncototient


 * Definition:Nontotient