A185176 - OEIS

%I #19 Sep 03 2023 11:12:51

%S 1,1,2,1,3,1,8,4,5,1,30,1,5,5,260,1,43,1,57,7,4,1,1930,8,10,99,93,1,

%T 223,1

%N a(n) = maximal number of different Galois groups with that same order for polynomials of degree n.

%C For prime p, a(p)=1.

%C For nonprime n, the most frequently seen orders are:

%C    4 = 4,

%C    6 = 24,

%C    8 = 32,

%C    9 = 54,

%C   10 = 200,

%C   12 = 192,

%C   14 = 2688,

%C   15 = 360,

%C   16 = 256,

%C   18 = 1296,

%C   20 = {5120,40000},

%C   21 = 30618,

%C   22 = 2420,

%C   24 = 1536,

%C   25 = {500,2500,12500},

%C   26 = 4056,

%C   27 = 4374,

%C   28 = 114688,

%C   30 = 24000000

%e a(4)=2 because for polynomials of degree 4, there are two different groups of order 4.

%e a(20)=57 because for polynomials of degree 20, there are 57 different groups of order 5120 and 57 different groups of order 40000.

%Y Cf. A002106, A177244, A186277, A186306, A186307, A186308.

%K nonn,hard

%O 2,3

%A _Artur Jasinski_, Feb 19 2011