# Only One Divides

**Computer Science**Level 3

A sequence of numbers is formed. Each positive integer in increasing order, except 1, is

added to the sequence if at most one term of the sequence divides it or

not added to the sequence if at least two terms of the sequence divide it.

The sequence begins \(2,3,4,5,7,\cdots\). Find the *last three digits* of the \(2013^{th}\) term of the sequence.