A298703 Numbers n such that number of groups of order n exceeds phi(n) (count numbers <= n and prime to n).

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

Offset

1,1

Links

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

Formula

Sequence is { n | A000001(n) > A000010(n) }.

Example

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.
...

Maple

with(GroupTheory): with(numtheory):
select(n -> NumGroups(n) > phi(n), [$1..850]);

Mathematica

Q[n_] := FiniteGroupCount@ n > EulerPhi@ n; Select[ Range@840, fQ] (* Robert G. Wilson v, Feb 13 2018 *)

Prog

(GAP) Filtered([1..850], n -> NumberSmallGroups(n) > Phi(n));

Crossrefs

Cf. A000001, A000010.

Sequence in context: A186407 A190037 A110558 * A273800 A273798 A163283

Adjacent sequences: A298700 A298701 A298702 * A298704 A298705 A298706

Keyword

nonn

Author

Muniru A Asiru, Jan 29 2018

Status

approved