A Triangle Based On Coprimality

[Leroy Quet]

[posted too to sci.math.]

Consider the following triangle of integers:

1
2  3
5  7  11
4  6  8  9
13 17 19 23 25
12 14 16 18 21 22
....

The top row is a 1.
The m_th row of the triangle contains the lowest m as-yet-unused positive 
integers, in order from left to right, which are each coprime with every 
integer in the (m-1)th row.

(Triangle not in the EIS, it seems.)

Is there a relatively easy way to determine in which row the integer k 
appears?

thanks,
Leroy Quet