Let's consider a Farey sequence: $$F_{n}=\{a_{1},...,a_{k}\}$$;
Where given elements satisfy definition of $n$-th Farey sequence.
My problem: Find the formula for the following sum: $$\sum_{l=1}^{k}a_{l}^{2}=?$$ Alternatively find asymptotic growth in dependence of $n$.
Only thing i know is that denominator of this sum is $(n!)^{2}$.
Regards.