A131932 Number of nonisomorphic nonsolvable groups of order A056866(n).

1, 3, 1, 1, 8, 1, 3, 6, 1, 26, 2, 2, 5, 2, 8, 23, 1, 6, 1, 107, 6, 1, 14, 1, 1, 1, 19, 2, 8, 28, 1, 93, 2, 4, 5, 5, 22, 1, 10, 1, 1, 588, 2, 20, 5, 1, 64, 4, 1, 5, 2, 5, 81, 1, 1, 18, 1, 25, 112, 2, 5, 1, 1

Offset

1,2

References

O. L. Hoelder, Bildung zusammengesetzter Gruppen, Math. Ann., 46 (1895), 321-422; see p. 420.

Links

Table of n, a(n) for n=1..63.

Example

a(1) = 1 because there is only 1 nonisomorphic and nonsolvable group of order 60: A_5 (alternating group of 5th degree).
a(2) = 3 because there are 3 different nonisomorphic and nonsolvable groups of order 120.

Prog

(GAP) NrUnsolvable := function(n) local i, count; count := 0; for i in [1..NumberSmallGroups(n)] do if not IsSolvableGroup(SmallGroup(n, i)) then count := count + 1; fi; od; return count; end; # Eric M. Schmidt, Apr 04 2013
(GAP) LoadPackage("GrpConst"); NrUnsolvable := function(n) local i, j, num; num := 0; for i in DivisorsInt(n) do if i<>1 then for j in [1..NrPerfectGroups(i)] do num := num + Length(Remove(UpwardsExtensions(PerfectGroup(IsPermGroup, i, j), n/i))); od; fi; od; return num; end; # Eric M. Schmidt, Nov 14 2013

Crossrefs

Cf. A001034, A060793, A056866, A056868.

Sequence in context: A297191 A147990 A134567 * A016462 A348693 A198618

Adjacent sequences: A131929 A131930 A131931 * A131933 A131934 A131935

Keyword

nonn

Author

Artur Jasinski, Jul 30 2007, Oct 20 2007

Extensions

Edited by N. J. A. Sloane, Oct 08 2007

More terms from Eric M. Schmidt, Apr 04 2013

a(44)-a(63) from Eric M. Schmidt, Nov 14 2013

Status

approved