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A282673 The number of groups of order n that are not Lagrangian. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A181000 A061853 A010104 * A280051 A030121 A320659

Adjacent sequences:  A282670 A282671 A282672 * A282674 A282675 A282676

KEYWORD

nonn

AUTHOR

W. Edwin Clark, Feb 20 2017

STATUS

approved

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Last modified February 17 15:19 EST 2019. Contains 320220 sequences. (Running on oeis4.)