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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 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.)