There is an easy way to do this

Firstly, we need to find the number of multiples of 13 that fit into $10^{6}$ , then add the multiples of $13^{2}$ (as we have not counted the second multiple of 13) and so on to give: $\displaystyle\sum_{n=1}^{\infty} \lfloor\frac{10^6}{13^n}\rfloor = 76923 +5917+455+35+2 + (0+0+0...) = \boxed{83332}$