1,36

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

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

(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;;

Sequence in context: A181000 A061853 A010104 * A280051 A030121 A320659

Adjacent sequences: A282670 A282671 A282672 * A282674 A282675 A282676

nonn

W. Edwin Clark, Feb 20 2017

approved