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A282673 The number of groups of order n that are not Lagrangian. 0


%S 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,

%T 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,

%U 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

%N The number of groups of order n that are not Lagrangian.

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

%H Mathematics StackExchange Discussion, <a href="http://math.stackexchange.com/questions/2144077/complete-classification-of-the-groups-for-which-converse-of-lagranges-theorem-h">Complete classification of the groups for which converse of Lagrange's Theorem holds</a>

%o (GAP)

%o a:=function(n)

%o local i,N,G,m;

%o N:=NumberSmallGroups(n);

%o m:=0;

%o for i in [1..N] do

%o G:=SmallGroup(n,i);

%o if Set(List(ConjugacyClassesSubgroups( G ),t->Size(Representative(t)))<>DivisorsInt(n)

%o then m:=m+1; fi;

%o od;

%o return m;

%o end;;

%K nonn

%O 1,36

%A _W. Edwin Clark_, Feb 20 2017

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Last modified March 20 23:22 EDT 2019. Contains 321354 sequences. (Running on oeis4.)