%I A059773
%S A059773 1,1,2,6,4,6,6,168,48,20,10,24,12,42,8,20160,16
%N A059773 Maximum size of Aut(G) where G is a finite group of order n.
%C A059773 If n = 2^k then take G to be (Z/2Z)^k, the Abelian group with n=2^k elements 
               and characteristic two. It is generated by any k linearly independent 
               (non-identity) elements, so the automorphism group has size (n-1)(n-2)(n-4)...(n-2^(k-1)), 
               which grows as n^log n. I think one can show that this is optimal 
               for n=2^k and furthermore that this has the highest rate of growth 
               for any infinite sequence of n's - Michael Kleber (michael.kleber(AT)gmail.com), 
               Feb 21, 2001.
%e A059773 The corresponding groups are 1, Z2, Z3, (Z2)^2, Z5, S3, Z7, (Z2)^3, (Z3)^2, 
               D5, Z11, A4, Z13, D7, Z15, (Z2)^4, Z17, ...
%Y A059773 Sequence in context: A065630 A110633 A119250 this_sequence A127399 A151689 
               A088438
%Y A059773 Adjacent sequences: A059770 A059771 A059772 this_sequence A059774 A059775 
               A059776
%K A059773 nonn,nice,more
%O A059773 1,3
%A A059773 Victor Miller (victor(AT)idaccr.org), Feb 21 2001
%E A059773 More terms from Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 09 2001