155141

The answer is:
4,4,2,6,3,3,1,5,5

First, I worked out that 4 and 5 must be at either end. This is because they are the largest red numbers so they can not be factors of any blue numbers other than themselves.
Then, I found the ant factors of the blue numbers of the list of red numbers.
6=3,2 (One could also be added although it is used at another point.)
5=5,1
4=4,2
3=3,1
Finally, I linked the factors which I had found for each of the blue numbers together whenever a number was repeated, taking into account the positions of 5 and 4.
4,2,3,1,5
I then inserted the blue numbers at alternating positions between the factors.