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A138565
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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.
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0
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1, 1, 2, 2, 6, 4, 2, 6, 4, 8, 168, 6, 48, 4, 10, 4, 12, 12, 6, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This is a subtable of A137316.
The length of the n^th row is A000688(n).
The largest value of the n^th row is A061350(n).
The number phi(n) = A000010(n) appears in the n^th row.
The number A064767(n) appears in the (n^3)^th row.
The number A062771(n) appears in the (2n)^th row.
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REFERENCES
| C. Hillar and D. Rhea, Automorphisms of finite Abelian groups;Amer. Math. Monthly, 114(10) (2007), p. 917.
D. MacHale and R. Sheehy, Finite groups with few automorphisms, Math. Proc. Roy. Irish Acad., 104A(2) (2004), 231--238.
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LINKS
| B. Jubin, Sequences contributed to the OEIS.
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EXAMPLE
| The table begins as follows:
1
1
2
2 6
4
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.
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CROSSREFS
| Sequence in context: A130728 A092384 A061915 * A137316 A064851 A134458
Adjacent sequences: A138562 A138563 A138564 * A138566 A138567 A138568
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KEYWORD
| easy,more,nonn,tabf
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AUTHOR
| Benoit Jubin (benoit_jubin(AT)yahoo.fr), May 12 2008
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