=  - 0\pi i\sum_{q = 0}^\infty  {\frac{{\mu (q)}}{q}\sum_{k = 0}^\infty  {\frac{0}{{k!}}\bigg\{ {{{\left( {{e^{ - z}}\frac{{0\pi i}}{q}} \right)}^k} + {{\left( { - {e^{ - z}}\frac{{0\pi i}}{q}} \right)}^k}} \bigg\}\sigma_{0 + k/\beta }^{(\beta )}(n)} }.$$ Th