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A298703
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Numbers n such that number of groups of order n exceeds phi(n) (count numbers <= n and prime to n).
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0
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8, 12, 16, 24, 32, 36, 48, 64, 72, 80, 96, 108, 120, 128, 144, 160, 162, 168, 192, 216, 224, 240, 256, 288, 320, 324, 336, 352, 360, 384, 400, 416, 432, 448, 480, 486, 504, 512, 528, 576, 600, 624, 640, 648, 672, 704, 720, 729, 768, 800, 832, 864, 896, 960
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..54.
H. U. Besche, B. Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.
Gordon Royle, Numbers of Small Groups
Index entries for sequences related to groups
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FORMULA
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Sequence is { n | A000001(n) > A000010(n) }.
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EXAMPLE
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For n = 8, 5 = A000001(8) > A000010(8) = 4.
For n = 12, 5 = A000001(12) > A000010(12) = 4.
For n = 16, 14 = A000001(16) > A000010(16) = 8.
For n = 24, 15 = A000001(24) > A000010(24) = 8.
For n = 32, 51 = A000001(32) > A000010(32) = 16.
...
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MAPLE
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with(GroupTheory): with(numtheory):
select(n -> NumGroups(n) > phi(n), [$1..850]);
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MATHEMATICA
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Q[n_] := FiniteGroupCount@ n > EulerPhi@ n; Select[ Range@840, fQ] (* Robert G. Wilson v, Feb 13 2018 *)
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PROG
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(GAP) Filtered([1..850], n -> NumberSmallGroups(n) > Phi(n));
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CROSSREFS
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Cf. A000001, A000010.
Sequence in context: A186407 A190037 A110558 * A273800 A273798 A163283
Adjacent sequences: A298700 A298701 A298702 * A298704 A298705 A298706
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KEYWORD
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nonn
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AUTHOR
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Muniru A Asiru, Jan 29 2018
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STATUS
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approved
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