15. Let $p=\sum_{k=1}^{6} k \ln k, \mathrm{e}^{p}$ be an integer, and $2^{n} \| \mathrm{e}^{p}$. Then $n=(\quad)$.
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
15. C.

Notice,
$$
p=\sum_{k=1}^{6} k \ln k=\ln \left(1^{1} \times 2^{2} \times 3^{3} \times 4^{4} \times 5^{5} \times 6^{6}\right) \text {. }
$$

Then $\mathrm{e}^{p}=\mathrm{e}^{\ln \left(1^{1} \times 2^{2} \times 3^{3} \times 4^{4} \times 5^{5} \times 6^{6}\right)}$
$$
\begin{array}{l}
=1^{1} \times 2^{2} \times 3^{3} \times 4^{4} \times 5^{5} \times 6^{6} \\
=2^{16} \times 3^{9} \times 5^{5} .
\end{array}
$$

Also, $2^{n} \| \mathrm{e}^{p}$, thus, $n=16$.