I made this today:
$$\boxed{N(t)=\frac{1}{n^c}\left(\vartheta (t)-\Re\left(\sum _{n=1}^{\text{nn}} \left(\underset{d \mid n}{\sum\limits_{d=1}^{n}} \left(f(\frac{1}{2}+it, d)-f(\frac{1}{2}+i0, d) \right)\right)\right)\right)}$$
$$f(s,d)=-i \mu (d) \left(\sum _{n=0}^{q-1} \left(\sum _{i=0}^{2 n+1} -\frac{d B_{2 (n+1)} k^{-2 n-1} \left|S_{2 n+1}^{(i)}\right| \log ^{-i-1}(d k) \Gamma (i+1,s \log (k d))}{(2 (n+1))!}\right)+\sum _{n=2}^k -\frac{d^{1-s} n^{-s}}{\log (d)+\log (n)}+\text{If}\left[d=1 \text{ then } 0\text{ else }-\frac{1^{-s} d^{1-s}}{\log (d)+\log (1)}\right]+\frac{d^{1-s} k^{-s}…