ÖMO 2008 Problem 5

Which positive integers are missing in the sequence $\left\{a_n\right\}$ , with $a_n = n + \left[\sqrt n\right] +\left[\sqrt [3]n\right]$ for all $n \ge 1$ ? ( $\left[x\right]$ denotes the largest integer less than or equal to $x$ , i.e. $g$ with $g \le x < g + 1$ .)