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A137316 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 nondecreasing. 1
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, 8, 16, 16, 16, 32, 32, 32, 32, 48, 64, 96, 192, 192, 20160, 16, 6, 12, 48, 54, 432, 18, 8, 20, 24, 40, 40, 12, 42, 10, 110, 22, 8, 16, 16, 24, 24, 24, 24, 24, 24, 48, 48, 48, 48, 144, 336 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..74.

D. MacHale and R. Sheehy, Finite groups with few automorphisms, Math. Proc. Roy. Irish Acad., 104A(2) (2004), 231--238.

EXAMPLE

The table begins as follows:

   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

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.

PROG

(GAP4) Print("\n") ;

for o in [ 1 .. 33 ] do

    n := NumberSmallGroups(o) ;

    og := [] ;

    for i in [1 .. n] do

        g := SmallGroup(o, i) ;

        H := AutomorphismGroup(g) ;

        ho := Order(H) ;

        Add(og, ho) ;

    od;

    Sort(og) ;

    Print(og) ;

    Print("\n") ;

od; # R. J. Mathar, Jul 13 2013

CROSSREFS

Cf. A064767, A060249, A060817, A062771, A060249, A002618, A061350.

Sequence in context: A092384 A061915 A138565 * A064851 A305353 A134458

Adjacent sequences:  A137313 A137314 A137315 * A137317 A137318 A137319

KEYWORD

nonn,tabf

AUTHOR

Benoit Jubin, Apr 06 2008, Apr 15 2008

STATUS

approved

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Last modified April 6 21:24 EDT 2020. Contains 333286 sequences. (Running on oeis4.)