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

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

Links

Table of n, a(n) for n=2..31.

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

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

Sequence in context: A140966 A058036 A136179 * A198315 A126761 A090559

Adjacent sequences: A185173 A185174 A185175 * A185177 A185178 A185179

Keyword

nonn,hard

Author

Artur Jasinski, Feb 19 2011

Status

approved