AMC 12 2002b Problem 21

For all positive integers $n$ less than $2002$, let \begin{eqnarray*} a_n =\left{ \begin{array}{lr} 11, & \text{if\ }n\ \text{is\ divisible\ by\ }13\ \text{and\ }14;\ 13, & \text{if\ }n\ \text{is\ divisible\ by\ }14\ \text{and\ }11;\ 14, & \text{if\ }n\ \text{is\ divisible\ by\ }11\ \text{and\ }13;\ 0, & \text{otherwise}. \end{array} \right. \end{eqnarray*} Calculate $\sum_{n=1}^{2001} a_n$. $\mathrm{(A)}\ 448 \mathrm{(B)}\ 486 \mathrm{(C)}\ 1560 \mathrm{(D)}\ 2001 \mathrm{(E)}\ 2002$