A map $\varphi:\mathbb{R}^n\to\mathbb{R}^n$ preserves harmonic functions if $f\circ\varphi$ is harmonic for every harmonic function $f:\mathbb{R}^n\to\mathbb{R}$.
It is known that these maps are, in fact, compositions of isometries and dilations.
I am looking for a concrete reference of this result, because I only have the reference included in Composition of a harmonic function with a holomorphic function where the bakground is Riemanian Manifolds. In spanish, we say that this is "matar moscas a cañonazos" (to kill a fly with a cannon). I mean, I have the feeling that this is a classical result of harmonic fuicntions, but I haven't found a "classical" reference.