$$f(n)=\sum\limits_{k=2}^{2^n}\small\left(k\cdot\left[\frac{1}{1 \left|k-2 \sum\limits_{i=1}^{k-1}\left[-\left\{\frac{k}{i}\right\}\right]\right|}\right]\cdot \left[\frac{1}{1 \left|n - \sum\limits_{j=2}^{k}\left[\frac{1}{1 \left|j-2 \sum\limits_{i=1}^{j-1}\left[-\left\{\frac{j}{i}\right\}\right]\right|}\right] \right| } \right] \right) $$