# Order of Divisor Function

## Theorem

For all $x \ge 1$:

- $\displaystyle \sum_{n \mathop \le x} d \left({n}\right) = x \log x + \left({2 \gamma-1}\right) x + O \left({\sqrt x}\right)$

where $\gamma$ is the Euler-Mascheroni constant and $d \left({n}\right)$ is the divisor function.