A370421 - OEIS

%I #16 Apr 08 2024 19:05:18

%S 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 39,41,42,43,44,45,46,47,49,51,52,53,55,57,58,59,61,62,63,65,66,67,68,

%U 69,70,71,73,74,75,76,77,78,79,82,83,85,86,87,89,91,92,93,94,95,97,99

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

%C This sequence is infinite. All primes other than 2 appear in the sequence.

%H Robin Jones, <a href="/A370421/b370421.txt">Table of n, a(n) for n = 1..782</a>

%o (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 i:=1;

%o while i lt 1024 do  // terms up to 1023

%o     inSequence:=1;

%o     j:=1;

%o     while j le NumberOfSmallGroups(i) do //iterate through all the groups of order i

%o         G:=SmallGroup(i,j);

%o         if #AllSubgroups(G) ge i then //some group has >= i subgroups

%o             inSequence:=0;

%o             break;

%o         end if;

%o         j:=j+1;

%o     end while;

%o     if inSequence eq 1 then

%o         i;

%o     end if;

%o     i:=i+1;

%o end while;

%Y Cf. A368538, A370422.

%K nonn

%O 1,1

%A _Robin Jones_, Feb 18 2024