# Category:Euler Phi Function

This category contains results about the Euler $\phi$ function.

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:

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