This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370423 #21 Sep 15 2024 20:22:57 %S A370423 1,2,6,28,260 %N A370423 Integers k such that the maximum number of subgroups of a group of order k is exactly k. %C A370423 Intersection of A368538 and A370422. Difference of A370422 and A370421. %C A370423 a(6) > 2000 if it exists. %o A370423 (Magma) // to get the terms up to 1023. %o A370423 i:=1; %o A370423 while i lt 1024 do // terms up to 1023 %o A370423 allGroupsHaveLessThanOrEqualNumberOfSubgroups:=1; %o A370423 someGroupWithExactNumberOfSubgroups:=0; %o A370423 j:=1; %o A370423 while j le NumberOfSmallGroups(i) do //iterate through all the groups of order i %o A370423 G:=SmallGroup(i, j); %o A370423 if #AllSubgroups(G) eq i then %o A370423 someGroupWithExactNumberOfSubgroups:=1; %o A370423 end if; %o A370423 if #AllSubgroups(G) gt i then //some group has > i subgroups %o A370423 allGroupsHaveLessThanOrEqualNumberOfSubgroups:=0; %o A370423 break; %o A370423 end if; %o A370423 j:=j+1; %o A370423 end while; %o A370423 if allGroupsHaveLessThanOrEqualNumberOfSubgroups eq 1 and someGroupWithExactNumberOfSubgroups eq 1 then %o A370423 i; %o A370423 end if; %o A370423 i:=i+1; %o A370423 end while; %Y A370423 Cf. A368538, A370421, A370422. %K A370423 nonn,more %O A370423 1,2 %A A370423 _Robin Jones_, Feb 18 2024