cp's OEIS Frontend

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

%I A124900 #18 Mar 12 2020 07:07:51
%S A124900 1,2,6,24,20,72,42,1152,1296,800,110,82944,156,3528,155520,7962624,
%T A124900 272,2239488,342,159252480,11757312,225280,506,13759414272,64000000,
%U A124900 1277952,13060694016,192631799808,812,48372940800
%N A124900 Largest order of any solvable transitive Galois group for an irreducible polynomial of degree n.
%C A124900 These transitive groups are in classification of MAGMA:
%C A124900 a(1)=1T1,a(2)=2T1,a(3)=3T2,a(4)=4T5,a(5)=5T3,a(6)=6T13,
%C A124900 a(7)=7T4,a(8)=8T47,a(9)=9T31,a(10)=10T33,a(11)=11T4,
%C A124900 a(12)=12T294,a(13)=13T6,a(14)=14T45,a(15)=15T87,
%C A124900 a(16)=16T1947,a(17)=17T5,a(18)=18T945,a(19)=19T6,
%C A124900 a(20)=20T1067,a(21)=21T142,a(22)=22T37,a(23)=23T5,
%C A124900 a(24)=24T24921,a(25)=25T179,a(26)=26T79,a(27)=27T2372,
%C A124900 a(28)=28T1773,a(29)=29T6,a(30)=30T5358.
%C A124900 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
%e A124900 a(9)=1296 because solvable Galois group T9_31 (in MAGMA's list) has order 1296
%Y A124900 Cf. A099732, A124901, A186772.
%K A124900 nonn
%O A124900 1,2
%A A124900 _Artur Jasinski_, Nov 12 2006
%E A124900 a(11)-a(30) from _Artur Jasinski_, Feb 26 2011