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A185176
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a(n) = maximal number of different Galois groups with that same order for polynomials of degree n.
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0
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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
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OFFSET
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2,3
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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STATUS
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approved
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