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The totient divisor-sum identity and multiplication of absolutely convergent Dirichlet series give the quotient for $\mathrm{Re}s>2$. The bound $\varphi (n)\le n$ proves convergence there. The simple pole of the Riemann zeta function at one makes the quotient unbounded as real $s\downarrow 2$. Since the coefficients are nonnegative, convergence at two would bound all these larger-real-part values, a contradiction. Thus the abscissa of absolute convergence of a Dirichlet series is two.

A truncated Perron integral over $c-iT$ to $c+iT$ recovers a summatory function with an error controlled by