A282673 The number of groups of order n that are not Lagrangian.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0

Offset

1,36

Comments

A group of order n is Lagrangian if it has a subgroup of order d for each divisor d of n.

Links

Table of n, a(n) for n=1..100.

Mathematics StackExchange Discussion, Complete classification of the groups for which converse of Lagrange's Theorem holds

Prog

(GAP)
a:=function(n)
local i, N, G, m;
N:=NumberSmallGroups(n);
m:=0;
for i in [1..N] do
G:=SmallGroup(n, i);
if Set(List(ConjugacyClassesSubgroups( G ), t->Size(Representative(t)))<>DivisorsInt(n)
then m:=m+1; fi;
od;
return m;
end;;

Crossrefs

Sequence in context: A335453 A061853 A010104 * A327159 A280051 A030121

Adjacent sequences: A282670 A282671 A282672 * A282674 A282675 A282676

Keyword

nonn

Author

W. Edwin Clark, Feb 20 2017

Status

approved