2017 Cayley Problem 25

A positive integer n with n \geq 3 is called a *Nella number* if there exists a positive integer x with x < n and there exists a positive integer m such that

- m is not divisible by x or by x+1, and - m is divisible by every other positive integer between 1 and n inclusive.

For example, n = 7 is a Nella number. How many Nella numbers n are there with 50 \leq n \leq 2017?

\textbf{(A)}\ 393\quad \textbf{(B)}\ 394\quad \textbf{(C)}\ 395\quad \textbf{(D)}\ 396\quad \textbf{(E)}\ 397

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.