We denote $\varphi$ the Euler totient function, defined by: $$\forall n \in \mathbb{N}^*, \quad \varphi(n) = \operatorname{card}\{k \in \llbracket 1, n \rrbracket \mid k \wedge n = 1\}$$ Prove that $\varphi = \mu * \mathbf{I}$.
We denote $\varphi$ the Euler totient function, defined by:
$$\forall n \in \mathbb{N}^*, \quad \varphi(n) = \operatorname{card}\{k \in \llbracket 1, n \rrbracket \mid k \wedge n = 1\}$$
Prove that $\varphi = \mu * \mathbf{I}$.