Define the function f_{1} on the positive integers by setting f_{1}(1)=1 and if n=p_{1}^{e_{1}} p_{2}^{e_{2}} \cdots p_{k}^{e_{k}} is the prime factorization of n>1, then
f_{1}(n)=\left(p_{1}+1\right)^{e_{1}-1}\left(p_{2}+1\right)^{e_{2}-1} \cdots\left(p_{k}+1\right)^{e_{k}-1}
For every m \geq 2, let f_{m}(n)=f_{1}\left(f_{m-1}(n)\right). For how many N in the range 1 \leq N \leq 400 is the sequence \left(f_{1}(N), f_{2}(N), f_{3}(N), \ldots\right) unbounded?
Note: a sequence of positive numbers is unbounded if for every integer B, there is a member of the sequence greater than B.
Answer Choices
A. 15
B. 16
C. 17
D. 18
E. 19