A124900 Largest order of any solvable transitive Galois group for an irreducible polynomial of degree n.

1, 2, 6, 24, 20, 72, 42, 1152, 1296, 800, 110, 82944, 156, 3528, 155520, 7962624, 272, 2239488, 342, 159252480, 11757312, 225280, 506, 13759414272, 64000000, 1277952, 13060694016, 192631799808, 812, 48372940800

Offset

1,2

Comments

These transitive groups are in classification of MAGMA:

a(1)=1T1,a(2)=2T1,a(3)=3T2,a(4)=4T5,a(5)=5T3,a(6)=6T13,

a(7)=7T4,a(8)=8T47,a(9)=9T31,a(10)=10T33,a(11)=11T4,

a(12)=12T294,a(13)=13T6,a(14)=14T45,a(15)=15T87,

a(16)=16T1947,a(17)=17T5,a(18)=18T945,a(19)=19T6,

a(20)=20T1067,a(21)=21T142,a(22)=22T37,a(23)=23T5,

a(24)=24T24921,a(25)=25T179,a(26)=26T79,a(27)=27T2372,

a(28)=28T1773,a(29)=29T6,a(30)=30T5358.

Conjecture: The sequence a(prime(n)), which begins 2, 6, 20, 42, 110, 156, 272, 342, 506, 812, increases without bound. It appears that a(prime(n)) may equal prime(n)(prime(n)-1), which is A036689. - Artur Jasinski, Feb 26 2011

Links

Table of n, a(n) for n=1..30.

Example

a(9)=1296 because solvable Galois group T9_31 (in MAGMA's list) has order 1296

Crossrefs

Cf. A099732, A124901, A186772.

Sequence in context: A363962 A319544 A354833 * A068819 A060068 A099732

Adjacent sequences: A124897 A124898 A124899 * A124901 A124902 A124903

Keyword

nonn

Author

Artur Jasinski, Nov 12 2006

Extensions

a(11)-a(30) from Artur Jasinski, Feb 26 2011

Status

approved