The Landau function G(n).

G(n) is the maximum of the orders of the permutations
of an n-element set,
thus the maximum of the products n1 x ... x nt,
where n1,...,nt are coprime numbers
such that n1 + ... + nt = n.

 

Edmund Landau

(1877-1938)

 
n n! G(n)
1 1 1
2 2 2
3 6 3
4 24 4
5 120 6
6 720 6
7 5040 12
8 40320 15
9 362880 20
     
20 2432902008176640000 420