Totient Proportionality

Let $C(N)$ be the number of positive integer $n\le N$ such that $$\frac{n}{\varphi (n)}=\frac{\varphi (n)}{\varphi (\varphi (n))},$$ where $\varphi (n)$ is the totient function.

You are given that $C({10}^5)=342$.

Find $C({10}^{15})$.

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