MathDB
Divisibility Series

Source:

January 2, 2009

Problem Statement

For all positive integers n n less than 2002 2002, let a_n \equal{} \begin{cases} 11 & \text{if }n\text{ is divisible by }13\text{ and }14 \\ 13 & \text{if }n\text{ is divisible by }11\text{ and }14 \\ 14 & \text{if }n\text{ is divisible by }11\text{ and }13 \\ 0 & \text{otherwise} \end{cases} Calculate \sum_{n \equal{} 1}^{2001} a_n. <spanclass=latexbold>(A)</span> 448<spanclass=latexbold>(B)</span> 486<spanclass=latexbold>(C)</span> 1560<spanclass=latexbold>(D)</span> 2001<spanclass=latexbold>(E)</span> 2002 <span class='latex-bold'>(A)</span>\ 448 \qquad <span class='latex-bold'>(B)</span>\ 486 \qquad <span class='latex-bold'>(C)</span>\ 1560 \qquad <span class='latex-bold'>(D)</span>\ 2001 \qquad <span class='latex-bold'>(E)</span>\ 2002