A124938 Number of non-solvable transitive Galois groups for polynomials of degree n.

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, 617, 2, 1896, 4

Offset: 1

Author

Artur Jasinski, Nov 13 2006

Keywords

• nonn
• more

Comments

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

Examples

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

Crossrefs

Cf. A002106, A124937.

Programs

GAP

"a(15)= "; l:=AllTransitiveGroups(NrMovedPoints,15,IsSolvable,false); # Artur Jasinski, Feb 04 2007

Magma

for g in [1..45] do
G:=TransitiveGroup(10,g);
IsSolvable(G);
end for; /* Artur Jasinski, Dec 03 2013 */

Formula

a(n) = A002106(n) - A124937(n). - Michel Marcus, Nov 06 2013

Extensions

More terms from Artur Jasinski, Feb 04 2007

a(10) and a(12) corrected by Artur Jasinski, Dec 03 2013

More terms from Alois P. Heinz, Feb 02 2014