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Search: id:A137316
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| A137316 |
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Array read by rows: T(n,k) is the number of automorphisms of the k^th group of order n, where the ordering is such that the rows are non-decreasing. |
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+0
2
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| 1, 1, 2, 2, 6, 4, 2, 6, 6, 4, 8, 8, 24, 168, 6, 48, 4, 20, 10, 4, 12, 12, 12, 24, 12, 6, 42, 8
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The length of the n^th row is A000001(n).
The largest value of the n^th row is A059773(n).
The number phi(n) = A000010(n) appears in the n^th row.
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REFERENCES
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D. MacHale and R. Sheehy, Finite groups with few automorphisms, Math. Proc. Roy. Irish Acad., 104A(2) (2004), 231-238
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EXAMPLE
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The table begins as follows:
1
1
2
2 6
4
The first row with two numbers corresponds to the two groups of order 4, the cyclic group Z_4 and the Klein group Z_2 x Z_2, whose automorphism groups are respectively the group (Z_4)^x = Z_2 and the symmetric group S_3.
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CROSSREFS
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Cf. A064767, A060249, A060817, A062771, A060249, A002618, A061350.
Adjacent sequences: A137313 A137314 A137315 this_sequence A137317 A137318 A137319
Sequence in context: A092384 A061915 A138565 this_sequence A064851 A134458 A009279
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KEYWORD
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more,nonn,tabf
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AUTHOR
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Benoit Jubin (benoit_jubin(AT)yahoo.fr), Apr 06 2008, Apr 15 2008
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