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A370422 Integers k such that all groups of order k have at most k subgroups.

%I A370422 #17 Sep 15 2024 20:22:52
%S A370422 1,2,3,5,6,7,9,10,11,13,14,15,17,19,21,22,23,25,26,28,29,30,31,33,34,
%T A370422 35,37,38,39,41,42,43,44,45,46,47,49,51,52,53,55,57,58,59,61,62,63,65,
%U A370422 66,67,68,69,70,71,73,74,75,76,77,78,79,82,83,85,86,87,89,91,92,93,94,95,97,99
%N A370422 Integers k such that all groups of order k have at most k subgroups.
%C A370422 This sequence is infinite. All primes appear in the sequence.
%H A370422 Robin Jones, <a href="/A370422/b370422.txt">Table of n, a(n) for n = 1..787</a>
%o A370422 (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 A370422 i:=1;
%o A370422 while i lt 1024 do  // terms up to 1023
%o A370422 inSequence:=1;
%o A370422 j:=1;
%o A370422 while j le NumberOfSmallGroups(i) do //iterate through all the groups of order i
%o A370422 G:=SmallGroup(i, j);
%o A370422 if #AllSubgroups(G) gt i then //some group has > i subgroups
%o A370422     inSequence:=0;
%o A370422     break;
%o A370422 end if;
%o A370422 j:=j+1;
%o A370422 end while;
%o A370422 if inSequence eq 1 then
%o A370422     i;
%o A370422 end if;
%o A370422 i:=i+1;
%o A370422 end while;
%Y A370422 Cf. A368538, A370421.
%K A370422 nonn
%O A370422 1,2
%A A370422 _Robin Jones_, Feb 18 2024