# A continuation

Calculus Level 5

Above is the graph of $$\displaystyle y=\sum _{n=1}^x\gcd \left(x,n\right)$$.

As you can see, there is quite a number of points scattered along the line $$y=2x-1$$.

Within $$0 \le x \le k$$, let the number of points that lie on the line $$y=2x-1$$ be $$D_{k}$$

Find $\lim _{ k\rightarrow \infty }{ \sqrt [ k ]{ k{ D }_{ { e }^{ k } } } }$

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