Euler's totient of a prime power

A prime power keeps the proportion $1-1/p$ of its residues coprime.Suggest a slogan

For a prime $p$ and an integer $k\ge1$, the Euler totient of $p^k$ is \[ \phi(p^k)=p^{k-1}(p-1)=p^k\qty{1-\frac1p}. \]

An integer $m$ with $1\le m\le p^k$ fails to be coprime to $p^k$ exactly when $p\divides m$, and there are $p^{k-1}$ such multiples of $p$. So $\phi(p^k)=p^k-p^{k-1}$.