Identity related to the totient function:$\sum\limits_{k=1}^n\phi(k)\left\lfloor \frac{n}{k}\right\rfloor = \frac{n(n+1)}{2}$
Identity involving Euler's totient function: $\sum \limits_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}$