Only One Divides

Computer Science Level 3

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

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

  2. 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.


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