Search: id:A138565
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%I A138565
%S A138565 1,1,2,2,6,4,2,6,4,8,168,6,48,4,10,4,12,12,6,8
%N A138565 Array read by rows: T(n,k) is the number of automorphisms of the k^th 
               Abelian group of order n, where the ordering is such that the rows 
               are non-decreasing.
%C A138565 This is a subtable of A137316.
%C A138565 The length of the n^th row is A000688(n).
%C A138565 The largest value of the n^th row is A061350(n).
%C A138565 The number phi(n) = A000010(n) appears in the n^th row.
%C A138565 The number A064767(n) appears in the (n^3)^th row.
%C A138565 The number A062771(n) appears in the (2n)^th row.
%D A138565 C. Hillar and D. Rhea, Automorphisms of finite Abelian groups;Amer. Math. 
               Monthly, 114(10) (2007), p. 917.
%D A138565 D. MacHale and R. Sheehy, Finite groups with few automorphisms, Math. 
               Proc. Roy. Irish Acad., 104A(2) (2004), 231--238.
%H A138565 B. Jubin, <a href="http://math.berkeley.edu/~jubin/oeis.html">Sequences 
               contributed to the OEIS</a>.
%e A138565 The table begins as follows:
%e A138565 1
%e A138565 1
%e A138565 2
%e A138565 2 6
%e A138565 4
%e A138565 The first row with two numbers corresponds to the two Abelian groups 
               of order 4, the cyclic group C_4 and the Klein group C_2 x C_2, whose 
               automorphism groups are respectively the group (C_4)^x = C_2 and 
               the symmetric group S_3.
%Y A138565 Sequence in context: A130728 A092384 A061915 this_sequence A137316 A064851 
               A134458
%Y A138565 Adjacent sequences: A138562 A138563 A138564 this_sequence A138566 A138567 
               A138568
%K A138565 easy,more,nonn,tabf
%O A138565 1,3
%A A138565 Benoit Jubin (benoit_jubin(AT)yahoo.fr), May 12 2008

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