You've been done a disservice if your earlier teachers didn't even mention the existence of Gaussian units (a cm-gram-sec system with "rationalized""unrationalized" E&M). Not that I like them, but simply because they were very common in the mid twentieth century and they still have their adherents (some even on Physics SE).
The unit of charge goes by several names including "statCoulombs", and it folds the dimensionality of $k$ into the charge unit so that Columb's law takes on the form $$ \mathbf{F} = \frac{q_1 \,q_2}{r^2} \hat{\mathbf{r}}\,.$$ Several of Maxwell's equations take on the form a mathemtician would use. For instance Guass' Law becomes $$ \nabla \cdot \mathbf{E} = 4 \pi \rho \,,$$ and similar changes happen throughout. Adherents describe these forms as being nicer, but having grown up with SI units I still find them more natural.