Alexander Hulpke (hulpke(AT)math.colostate.edu), Feb 19 2002
sent an extension of this sequence:

%I A000019
%S A000019  1, 1, 2, 2, 5, 4, 7, 7, 11, 9, 8, 6, 9, 4, 6, 22, 10, 4, 8, 4, 9, 4, 7, 5, 
  28, 7, 15, 14, 8, 4, 12, 7, 4, 2, 6, 22, 11, 4, 2, 8, 10, 4, 10, 4, 9, 2, 
  6, 4, 40, 9, 2, 3, 8, 4, 8, 9, 5, 2, 6, 9, 14, 4, 8, 74, 13, 7, 10, 7, 2, 
  2, 10, 4, 16, 4, 2, 2, 4, 6, 10, 4, 155, 10, 6, 6, 6, 2, 2, 2, 10, 4, 10, 
  2, 2, 2, 2, 2, 14, 4, 2, 38, 11, 5, 10, 4, 11, 2, 6, 4, 14, 4, 2, 10, 12, 
  4, 2, 2, 5, 2, 4, 23, 57, 7, 2, 2, 45, 19, 15, 7, 4, 7, 10, 4, 3, 2, 5, 14, 
  10, 4, 10, 4, 2, 2, 2, 17, 2, 2, 2, 2, 8, 4, 14, 4, 6, 2, 3, 9, 14, 4, 2, 
  2, 2, 7, 12, 4, 7, 2, 6, 9, 75, 7, 6, 2, 8, 4, 6, 6, 2, 2, 6, 4, 20, 4, 4, 
  2, 2, 3, 2, 2, 2, 6, 10, 4, 16, 4, 2, 10, 11, 4, 14, 4, 2, 2, 3, 2, 2, 2, 
  2, 5, 2, 6, 18, 4, 2, 2, 2, 22, 2, 2, 2, 5, 2, 2, 10, 4, 12, 2, 6, 4, 14, 
  4, 6, 2, 10, 6, 2, 2, 2, 2, 10, 4, 22, 4, 36, 6, 2, 2, 2, 3, 2, 2, 10, 4, 
  9, 2, 4
%N A000019 Primitive permutation groups of degree n.
%C A000019 A check found errors in Theissen's data (degree 121 and 125) as well as in Short's work (degree 169).
%o A000019 (GAP) List([2..255],NrPrimitiveGroups);

*****************************************************************************

Colva M. Roney-Dougal sent 1000 terms on Jan 31 2003:


%I A000019
%S A000019 1, 1, 2, 2, 5, 4, 7, 7, 11, 9, 8, 6, 9, 4, 6, 22, 10, 4, 8, 4, 9, 4, 7, 5, 
28, 7, 15, 14, 8, 4, 12, 7, 4, 2, 6, 22, 11, 4, 2, 8, 10, 4, 10, 4, 9, 2, 
6, 4, 40, 9, 2, 3, 8, 4, 8, 9, 5, 2, 6, 9, 14, 4, 8, 74, 13, 7, 10, 7, 2, 
2, 10, 4, 16, 4, 2, 2, 4, 6, 10, 4, 155, 10, 6, 6, 6, 2, 2, 2, 10, 4, 10, 
2, 2, 2, 2, 2, 14, 4, 2, 38, 11, 5, 10, 4, 11, 2, 6, 4, 14, 4, 2, 10, 12, 
4, 2, 2, 5, 2, 4, 23, 57, 7, 2, 2, 45, 19, 15, 7, 4, 7, 10, 4, 3, 2, 5, 
14, 10, 4, 10, 4, 2, 2, 2, 17, 2, 2, 2, 2, 8, 4, 14, 4, 6, 2, 3, 9, 14, 4,
2, 2, 2, 7, 12, 4, 7, 2, 6, 9, 75, 7, 6, 2, 8, 4, 6, 6, 2, 2, 6, 4, 20, 4,
4, 2, 2, 3, 2, 2, 2, 6, 10, 4, 16, 4, 2, 10, 11, 4, 14, 4, 2, 2, 3, 2, 2, 
2, 2, 5, 2, 6, 18, 4, 2, 2, 2, 22, 2, 2, 2, 5, 2, 2, 10, 4, 12, 2, 6, 4, 
14, 4, 6, 2, 10, 6, 2, 2, 2, 2, 10, 4, 22, 4, 36, 6, 2, 2, 2, 3, 2, 2, 10,
4, 9, 2, 4, 244, 15, 4, 2, 2, 2, 2, 6, 4, 2, 3, 2, 2, 8, 4, 18, 4, 8, 2, 
4, 8, 14, 4, 2, 24, 18, 4, 10, 4, 3, 4, 2, 2, 97, 7, 2, 2, 8, 4, 2, 2, 4, 
2, 2, 11, 2, 2, 2, 2, 2, 2, 15, 4, 2, 2, 10, 4, 18, 4, 5, 2, 8, 4, 2, 2, 
2, 2, 2, 10, 14, 2, 2, 2, 2, 6, 18, 4, 2, 2, 2, 9, 22, 4, 2, 2, 4, 2, 90, 
8, 2, 2, 6, 4, 14, 4, 11, 2, 14, 4, 2, 2, 7, 2, 6, 20, 92, 7, 2, 11, 2, 2,
10, 4, 5, 2, 2, 2, 14, 4, 2, 2, 2, 11, 18, 4, 4, 2, 6, 4, 2, 2, 2, 2, 8, 
4, 2, 2, 2, 2, 2, 4, 20, 4, 2, 16, 17, 4, 2, 2, 2, 6, 2, 2, 18, 4, 2, 2, 
2, 2, 2, 7, 2, 2, 10, 4, 26, 4, 2, 2, 3, 2, 2, 2, 2, 2, 10, 4, 22, 4, 6, 
2, 2, 2, 10, 4, 24, 2, 10, 4, 2, 2, 2, 2, 16, 4, 2, 2, 2, 2, 4, 4, 18, 4, 
2, 2, 14, 8, 18, 4, 7, 2, 6, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 4, 2, 2, 
2, 10, 2, 2, 14, 4, 2, 2, 14, 4, 2, 2, 10, 12, 2, 2, 10, 4, 2, 2, 6, 8, 2,
3, 2, 2, 8, 4, 3, 58, 14, 2, 2, 2, 2, 2, 2, 9, 18, 4, 14, 4, 8, 2, 4, 9, 
65, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 26, 4, 2, 2, 2, 2, 18, 4, 2, 2, 2, 
2, 3, 2, 2, 2, 8, 4, 2, 6, 4, 2, 6, 4, 2, 2, 7, 2, 10, 4, 18, 4, 2, 2, 2, 
11, 23, 4, 2, 2, 2, 2, 2, 2, 6, 2, 6, 4, 2, 2, 2, 2, 12, 4, 4, 2, 2, 2, 
10, 4, 26, 4, 2, 2, 2, 2, 10, 4, 2, 2, 2, 2, 20, 4, 2, 4, 18, 4, 10, 5, 2,
2, 2, 2, 698, 10, 2, 2, 2, 4, 26, 4, 2, 2, 2, 2, 2, 2, 2, 2, 18, 4, 10, 4,
2, 2, 10, 4, 2, 2, 7, 2, 8, 4, 2, 2, 4, 2, 10, 9, 26, 4, 2, 2, 2, 6, 2, 2,
2, 2, 4, 8, 26, 4, 2, 30, 11, 4, 2, 4, 2, 2, 10, 4, 2, 2, 2, 2, 2, 2, 18, 
4, 6, 2, 2, 2, 2, 2, 2, 2, 20, 4, 6, 2, 2, 2, 2, 2, 14, 4, 2, 2, 2, 2, 4, 
2, 2, 2, 6, 4, 2, 2, 2, 2, 2, 2, 14, 4, 501, 15, 2, 2, 14, 4, 2, 2, 2, 2, 
14, 4, 4, 2, 10, 4, 2, 2, 2, 2, 2, 3, 18, 4, 2, 2, 2, 7, 28, 4, 3, 2, 18, 
4, 2, 2, 4, 2, 2, 2, 20, 4, 2, 2, 8, 4, 3, 2, 2, 2, 2, 4, 3, 2, 2, 38, 2, 
2, 10, 4, 2, 2, 2, 4, 2, 2, 2, 2, 8, 4, 2, 2, 2, 2, 2, 2, 2, 10, 2, 2, 10,
4, 22, 4, 2, 2, 2, 4, 2, 2, 8, 24, 14, 4, 10, 4, 2, 2, 10, 4, 20, 4, 2, 2,
2, 2, 2, 2, 2, 2, 6, 8, 116, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 14, 4, 2, 2,
10, 4, 18, 4, 6, 2, 6, 4, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 14, 4, 2, 3,
22, 4, 20, 4, 2, 2, 6, 4, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 10, 2, 2, 6, 2,
2, 2, 10, 4, 2, 5, 18, 4, 2, 2, 2, 2, 2, 2, 18, 4, 2, 2, 2, 2, 2, 2, 2, 2,
14, 4, 2, 2, 2, 2, 2, 2, 26, 4, 2, 2, 14, 4, 2, 2, 4, 6, 10, 4, 2, 2, 2, 
2, 18, 4, 2, 2, 2, 2, 2, 10, 134, 7, 2, 2, 2, 2, 18, 4, 4, 2, 10, 4, 2, 2,
2, 2, 12, 4, 2, 4, 2, 2, 6, 4, 2, 2, 2, 2, 2, 4, 26, 4, 4, 2, 2, 2, 14, 4,
2
%N A000019 The number of primitive groups of degree n.
%C A000019 This extends the sequence to degree 999.
%D A000019 Colva M. Roney-Dougal; William R Unger. The affine primitive groups of degree less than 1000. J. Symbolic Comput. To appear. 
%o A000019 (MAGMA) [NumberOfPrimitiveGroups(i) : i in [1..999]];
%A A000019 Colva M. Roney-Dougal (colva(AT)maths.usyd.edu.au), Jan 31 2003