cp's OEIS Frontend

A185176 a(n) = maximal number of different Galois groups with that same order for polynomials of degree n.

%I A185176 #19 Sep 03 2023 11:12:51
%S A185176 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 A185176 223,1
%N A185176 a(n) = maximal number of different Galois groups with that same order for polynomials of degree n.
%C A185176 For prime p, a(p)=1.
%C A185176 For nonprime n, the most frequently seen orders are:
%C A185176    4 = 4,
%C A185176    6 = 24,
%C A185176    8 = 32,
%C A185176    9 = 54,
%C A185176   10 = 200,
%C A185176   12 = 192,
%C A185176   14 = 2688,
%C A185176   15 = 360,
%C A185176   16 = 256,
%C A185176   18 = 1296,
%C A185176   20 = {5120,40000},
%C A185176   21 = 30618,
%C A185176   22 = 2420,
%C A185176   24 = 1536,
%C A185176   25 = {500,2500,12500},
%C A185176   26 = 4056,
%C A185176   27 = 4374,
%C A185176   28 = 114688,
%C A185176   30 = 24000000
%e A185176 a(4)=2 because for polynomials of degree 4, there are two different groups of order 4.
%e A185176 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 A185176 Cf. A002106, A177244, A186277, A186306, A186307, A186308.
%K A185176 nonn,hard
%O A185176 2,3
%A A185176 _Artur Jasinski_, Feb 19 2011