# Thread: 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)

Thank you in advance!

2. Sequence or series?

In any case, here's an example of a set whose elements (I think) satisfy the given conditions:

The set is generated by prime multiples of 6, 10, and 15. (i.e {6p | p is prime} U {10p | p is prime} U {15p | p is prime})

So it exists! (if I'm correct hehehe)

3. Thank you very much. I should'we written sequence, sorry, I always mix them up.
Thanks!