Tessellate S.T.E.M.S. (2019) - Mathematics - Category A (School) - Set 3 - Objective Problem 4

Suppose that $n$ and $k$ are positive integers such that $1 = \underbrace{\varphi( \varphi( \dots \varphi(}_{k\ \text{times}} n) \dots ))$ where $\varphi(n)$ denotes the number of elements of $\{1, \dots, n\}$ which are relatively prime to $n$ . Which of the following is the sharpest upper bound for $n$ ?

This problem is a part of Tessellate S.T.E.M.S. (2019)