A nontotient number is an even natural number $n$ for which $\varphi(x) = n$ has no solutions, where $\varphi(x)$ is the Euler totient function. The smallest nontotient numbers are $$14, 26, 34, 38, 50, 62, 68, 74, 76, 86, 90, 94, 98, 114, 118, 122, 124, 134, \ldots$$
I generated the $n$-th nontotient number $T_n$ for all $n$ upto $10^2, 10^3, 10^4, 10^5, 10^6$ and and observed that the relation between $n$ and $T_n$ was almost perfectly linear. To test this intuition further, I generted the data for $n$ upto $10^7$ but this time, I observed that somewhere at about $n \approx 5.6 \times 10^6$ the linear relation breaks down and $T_n$ starts grown at a super linear rate i.e. faster than $n$.
Question 1: What is known about the growth rate of $T_n$?
Question 2: What is happening at about $n = 5.6 \times 10^6$ when $T_n$ when starts to quickly deviate away from linearity?