= Solution
Let $F(s)=\sum_{n\geq1}a_nn^{-s}$ converge absolutely for $\Re s>\sigma_a$. <Perron formula> states that for $c>\sigma_a$ and nonintegral $x>0$,
$$
\sum_{n\leq x}a_n
=\frac1{2\pi i}\int_{c-i\infty}^{c+i\infty}
F(s)\frac{x^s}{s}\,ds,
$$
where the integral is understood as the limit of symmetric truncations under the usual convergence hypotheses. If $x$ is an integer, the endpoint term is counted with weight $1/2$. Effective versions truncate at height $T$ and include an explicit error depending on the coefficients and the distance of $x$ from nearby integers.
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