Math Help - Infinite series of positive integers - proving existence

1. Infinite series of positive integers - proving existence

Prove that a series exist with the following propeties:
- the series is infinite and contains of positive integers
- no elements divide any of the others in the series
- any two numbers have a >1 common divisor in the series
- but there are no >1 numbers that divides all the elements of the sereis (so the greatest common divisor of the elements is 1)