More Permuations & Inverses & Coprime Pairs

[Leroy Quet]

I was wondering what the sequence is where the nth term is the number of 
permutations, {b(k)}, of {1,2,3,...n} where each inverse permutation 
{c(k)}, is such that
GCD(b(k),c(k)) = 1 for all k, 1<=k<=n.

For example: If we have the permutation (for n=4) 2,4,1,3, its inverse is 
3,1,4,2.
Since GCD(2,3) = GCD(4,1) = GCD(1,4) = GCD(3,2) = 1, then these two 
permutations of 1,2,3,4 are included in the count.

Another permutation of 1,2,3,4, however, is 2,3,4,1 with an inverse of 
4,1,2,3.
Sonce GCD(2,4) = 2, these two permutations are not counted.

So I get the sequence beginning: 1,2,6,4,...

And since, for n >=2, all permutations of {1,2,...,n} which are counted 
also have a different inverse which is also counted, then we can also 
create the sequence where a(1)=1, and the other terms are all 1/2 of 
their respective terms in the original sequence.
So we have: 1,1,3,2,...

Are either of these sequences in the EIS?
If they are not, could someone please calculate/submit them?

thanks,
Leroy Quet