Question 21
For all positive integers $n$ less than $2002,$ let $$
a_n=\begin{cases} 11, & \text{if } n \text{ is divisible by } 13 \text{ and } 14;\\ 13, & \text{if } n \text{ is divisible by } 14 \text{ and } 11;\\ 14, & \text{if } n \text{ is divisible by } 11 \text{ and } 13;\\ 0, & \text{otherwise}. \end{cases}
$$ Calculate $\displaystyle\sum_{n=1}^{2001} a_n.$
a_n=\begin{cases} 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{cases}
$$ Calculate $\displaystyle\sum_{n=1}^{2001} a_n.$