A370423 Integers k such that the maximum number of subgroups of a group of order k is exactly k.

1, 2, 6, 28, 260

Offset: 1

Author

Robin Jones, Feb 18 2024

Keywords

• nonn
• more

Comments

Intersection of A368538 and A370422. Difference of A370422 and A370421.

a(6) > 2000 if it exists.

Crossrefs

Cf. A368538, A370421, A370422.

Programs

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;