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A370421 Integers k such that all groups of order k have strictly fewer than k subgroups.

%I A370421 #16 Apr 08 2024 19:05:18
%S A370421 3,5,7,9,10,11,13,14,15,17,19,21,22,23,25,26,29,30,31,33,34,35,37,38,
%T A370421 39,41,42,43,44,45,46,47,49,51,52,53,55,57,58,59,61,62,63,65,66,67,68,
%U A370421 69,70,71,73,74,75,76,77,78,79,82,83,85,86,87,89,91,92,93,94,95,97,99
%N A370421 Integers k such that all groups of order k have strictly fewer than k subgroups.
%C A370421 This sequence is infinite. All primes other than 2 appear in the sequence.
%H A370421 Robin Jones, <a href="/A370421/b370421.txt">Table of n, a(n) for n = 1..782</a>
%o A370421 (Magma) // to get the terms up to 1023. The program will not work for i=1024, returning a positive result, since those groups are not classified.
%o A370421 i:=1;
%o A370421 while i lt 1024 do  // terms up to 1023
%o A370421     inSequence:=1;
%o A370421     j:=1;
%o A370421     while j le NumberOfSmallGroups(i) do //iterate through all the groups of order i
%o A370421         G:=SmallGroup(i,j);
%o A370421         if #AllSubgroups(G) ge i then //some group has >= i subgroups
%o A370421             inSequence:=0;
%o A370421             break;
%o A370421         end if;
%o A370421         j:=j+1;
%o A370421     end while;
%o A370421     if inSequence eq 1 then
%o A370421         i;
%o A370421     end if;
%o A370421     i:=i+1;
%o A370421 end while;
%Y A370421 Cf. A368538, A370422.
%K A370421 nonn
%O A370421 1,1
%A A370421 _Robin Jones_, Feb 18 2024