geometry - Maximum relative quotient of radii of circles surrounding other circle touching neighbors exactly once?

Assume we have one circle with radius $R$ centered at origo $(0,0)$.

How big circles of radius $r$ can we put around it touching it and each neighbor in one and only one point each if we want to fit $N$ such circles?

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The only special case (own work) I know is if $r=R$ if $N=6$.

If iterated, it gives the famous hexagonal lattice of $2$ dimensional space.

Here is example for $N=6$.