Prime Number Formula XVI

p_n=1+\displaystyle\sum_{k=1}^{2\cdot (\lfloor n\ln(n) \rfloor+1)}\left(1-\left\lfloor \frac{1}{n}\cdot \displaystyle\sum_{j=2}^k \left(1+\left\lfloor \frac{2-\displaystyle\sum_{i=1}^j \left\lfloor \frac{\gcd(i,j)}{i} \right\rfloor}{j} \right\rfloor\right) \right\rfloor\right)

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