Symbols:Phi

Phi

Euler Phi Function

$\phi \left({n}\right)$

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

The totient, indicator or Euler $\phi$-function is the function $\phi: \Z_{>0} \to \Z_{>0}$ defined as:

$\phi \left({n}\right) = $ the number of integers less than or equal to $n$ which are prime to $n$

That is:

$\phi \left({n}\right) = \left|{S_n}\right|: S_n = \left\{{k: 1 \le k \le n, k \perp n}\right\}$

The $\LaTeX$ code for $\phi \left({n}\right)$ is \phi \left({n}\right).