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A185176
a(n) = maximal number of different Galois groups with that same order for polynomials of degree n.
0
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, 223, 1
OFFSET
2,3
COMMENTS
For prime p, a(p)=1.
For nonprime n, the most frequently seen orders are:
4 = 4,
6 = 24,
8 = 32,
9 = 54,
10 = 200,
12 = 192,
14 = 2688,
15 = 360,
16 = 256,
18 = 1296,
20 = {5120,40000},
21 = 30618,
22 = 2420,
24 = 1536,
25 = {500,2500,12500},
26 = 4056,
27 = 4374,
28 = 114688,
30 = 24000000
EXAMPLE
a(4)=2 because for polynomials of degree 4, there are two different groups of order 4.
a(20)=57 because for polynomials of degree 20, there are 57 different groups of order 5120 and 57 different groups of order 40000.
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Artur Jasinski, Feb 19 2011
STATUS
approved