%I A064527
%S A064527 1,2,4,6,8,12,16,18,24,32,36,48,54,64,72,96,108,120,128,144,162,192,
%T A064527 200,216,240,256,288,324,384,400
%N A064527 Numbers n such that there exists a finite group G such that all entries 
               in its character table are integers.
%C A064527 The list contains all numbers of the form 2^w*3^u for w> 0, u>=0. But 
               it also contains 120, 200, 240 and 400. It contains n! for all n 
               because the symmetric groups have integral character tables. By taking 
               direct products, we get all numbers of the form n! * 2^w * 3^u, w 
               >= 0, u >= 0. The 200 comes from a semidirect product of an elementary 
               group of order 25 with a quaternion group of order 8, with fixed-point-free 
               action (a Frobenius group). - Derek Holt
%Y A064527 Contains A000142 and A007694.
%Y A064527 Sequence in context: A140067 A067946 A145853 this_sequence A007694 A050622 
               A082662
%Y A064527 Adjacent sequences: A064524 A064525 A064526 this_sequence A064528 A064529 
               A064530
%K A064527 nonn,nice
%O A064527 1,2
%A A064527 Tim Brooks (tim_brooks(AT)my-deja.com), Oct 07 2001
%E A064527 More terms from Derek Holt (mareg(AT)csv.warwick.ac.uk), Oct 07, 2001