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A370423
Integers k such that the maximum number of subgroups of a group of order k is exactly k.
0
1, 2, 6, 28, 260
OFFSET
1,2
COMMENTS
Intersection of A368538 and A370422. Difference of A370422 and A370421.
a(6) > 2000 if it exists.
PROG
(Magma) // to get the terms up to 1023.
i:=1;
while i lt 1024 do // terms up to 1023
allGroupsHaveLessThanOrEqualNumberOfSubgroups:=1;
someGroupWithExactNumberOfSubgroups:=0;
j:=1;
while j le NumberOfSmallGroups(i) do //iterate through all the groups of order i
G:=SmallGroup(i, j);
if #AllSubgroups(G) eq i then
someGroupWithExactNumberOfSubgroups:=1;
end if;
if #AllSubgroups(G) gt i then //some group has > i subgroups
allGroupsHaveLessThanOrEqualNumberOfSubgroups:=0;
break;
end if;
j:=j+1;
end while;
if allGroupsHaveLessThanOrEqualNumberOfSubgroups eq 1 and someGroupWithExactNumberOfSubgroups eq 1 then
i;
end if;
i:=i+1;
end while;
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robin Jones, Feb 18 2024
STATUS
approved