# Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2

The following formula holds for $\mathrm{Re}(z) > 2$: $$\displaystyle\sum_{k=1}^{\infty} \dfrac{\phi(k)}{k^z} = \dfrac{\zeta(z-1)}{\zeta(z)},$$ where $\phi$ denotes the totient and $\zeta$ denotes the Riemann zeta function.