Documentation

Calculate Euler's totient function \(\phi(m)\).

Euler's so-called totient function \(\phi(m)\) is defined as the number of positive integers \(r\), where \(1 \leq r \leq m\), that are coprime to \(m\).

For example, with \(m = 10\), \(\{r \,|\, 1 \leq r \leq m, \textrm{coprime to $m$}\} = \{ 1, 3, 7, 9 \}\); thus \(\phi(m) = 4\). Note the special case of \(\phi(1) = 1\).

Examples

>>> totient 10
4