|
Search: id:A138565
|
|
|
| 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. |
|
+0
1
|
|
| 1, 1, 2, 2, 6, 4, 2, 6, 4, 8, 168, 6, 48, 4, 10, 4, 12, 12, 6, 8
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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.
|
|
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.
|
|
LINKS
|
B. Jubin, Sequences contributed to the OEIS.
|
|
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.
|
|
CROSSREFS
|
Adjacent sequences: A138562 A138563 A138564 this_sequence A138566 A138567 A138568
Sequence in context: A130728 A092384 A061915 this_sequence A137316 A064851 A134458
|
|
KEYWORD
|
easy,more,nonn,tabf
|
|
AUTHOR
|
Benoit Jubin (benoit_jubin(AT)yahoo.fr), May 12 2008
|
|
|
Search completed in 0.002 seconds
|
