Max GCD Permutation Product

[Ralf Stephan]

Leroy Quet:
> If we take a permutation [a(1),a(2),...a(m)] of
> [1,2,3,...m],
> 
> we can form the product:
> 
> P = product{k=1 to m} GCD(a(k),a(k-1)),
> 
> where a(0) = a(m).
> 
> But what would the maximum P be,taken over all permutations of the first 
> m positive integers?  
> 
> By hand, I get:
> 
> 1, 1, 1, 2, 2, 12, 12, 48, 144,...
> 
> which corresponds with sequence A025527,
> m!/LCM(1,2,3,...,m).

and also with A025557/2.


ralf