Consecutive Squarefrees, Not Coprime

[David Wilson]

The gcd of any two consecutive squarefree numbers must be squarefree.  Given 
the k-tuple conjecture, I can show that every squarefree number is in fact 
the gcd of two consecutive squarefrees (the k-tuple conjecture may not be 
necessary here).

This leads us immediately to ask, for squarefree n, what is the smallest a 
such that a and a+n are consecutive squarefrees with gcd(a, a+n) = n.  I get

n a(n)
1 1
2 422
3 174
5 22830
6 <=1292013541080148674
7 234374

I'm sure my bound on a(6) is rather loose and could be tightened with a 
little effort.  It is not out of the question that the exact value could be 
found.

a(10) seems hopeless.

a(11) would be about as hard as a(6).