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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