Editing Euler's totient function (section)

====Example====

:<math>\varphi(20)=\varphi(2^2 5)=20\,(1-\tfrac12)\,(1-\tfrac15)
=20\cdot\tfrac12\cdot\tfrac45=8.</math>

In words: the distinct prime factors of 20 are 2 and 5; half of the twenty integers from 1 to 20 are divisible by 2, leaving ten; a fifth of those are divisible by 5, leaving eight numbers coprime to 20; these are: 1, 3, 7, 9, 11, 13, 17, 19.

The alternative formula uses only integers:<math display="block">\varphi(20) = \varphi(2^2 5^1)= 2^{2-1}(2{-}1)\,5^{1-1}(5{-}1) = 2\cdot 1\cdot 1\cdot 4 = 8.</math>