= Totient Dirichlet series and its absolute convergence boundary
{title2=$\sum_{n\geq1}\phi(n)n^{-s}=\zeta(s-1)/\zeta(s),\quad\sigma_a=2$}
The <totient divisor-sum identity> and multiplication of absolutely convergent <Dirichlet series> give the quotient for $\operatorname{Re}s>2$. The bound $\phi(n)\leq n$ proves convergence there. The <simple pole> of the <Riemann zeta function> at one makes the quotient unbounded as real $s\downarrow2$. 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.
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