Given a positive integer $n>1$, do we have some bound on the sequence
$$a_n=\sum_{\chi\neq 1} \sum_{p} \frac{\chi(p)}{p},$$
where $\chi$ runs over the nontrivial characters modulo $n$ and $p$ runs over all primes.
This is a real number, since
$$\sum_{\chi\neq 1} \sum_{p} \frac{\chi(p)}{p^s}=\sum_{p\equiv1(n)}\frac{\phi(n)}{p^s}-\sum_{p}\frac{1}{p^s}.$$
Here $\phi$ is Euler's function. Since by Dirichlet's theorem, ratio of the two terms on the right is $1$ when $s\rightarrow 1$. So I say this is an error term.