A124938 - OEIS

%I #18 Sep 08 2022 08:45:28

%S 0,0,0,0,2,4,3,5,4,21,4,36,3,27,40,49,5,91,2,358,56,27,3,807,79,26,64,

%T 617,2,1896,4

%N Number of non-solvable transitive Galois groups for polynomials of degree n.

%C This sequence is A002106 (total number of transitive Galois groups) - A124937 (number of solvable transitive groups).

%F a(n) = A002106(n) - A124937(n). - _Michel Marcus_, Nov 06 2013

%e a(5) = 2: for polynomials of degree 5 we have 2 non-solvable groups: A_5 (T5_4) and S_5 (T5_5)

%o (GAP) "a(15)= ",l:=AllTransitiveGroups(NrMovedPoints,15,IsSolvable,false); - _Artur Jasinski_, Feb 04 2007

%o (Magma) for g in [1..45] do

%o G:=TransitiveGroup(10,g);

%o IsSolvable(G);

%o end for; /* _Artur Jasinski_, Dec 03 2013 */

%Y Cf. A002106, A124937.

%K nonn,more

%O 1,5

%A _Artur Jasinski_, Nov 13 2006

%E More terms from _Artur Jasinski_, Feb 04 2007

%E a(10) and a(12) corrected by _Artur Jasinski_, Dec 03 2013

%E More terms from _Alois P. Heinz_, Feb 02 2014