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%I #18 Nov 24 2019 03:14:22
%S 3,6,18,24,60,36,126,96,162,120,330,144,468,252,360,384,816,324,1026,
%T 480,756,660,1518,576,1500,936,1458,1008,2436,720,2790,1536,1980,1632,
%U 2520,1296,3996,2052,2808,1920,4920,1512,5418,2640,3240,3036,6486,2304,6174,3000,4896,3744,8268
%N Number of ordered pairs a,b of elements in the dihedral group D_2n such that the subgroup generated by the pair a,b is the entire group D_2n.
%H Kenneth G. Hawes, <a href="/A064400/b064400.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 3 * A002618(n) = 3 * n * phi(n).
%t Table[a=GroupElements[DihedralGroup[n]];Count[Flatten[Table[Table[GroupOrder[PermutationGroup[{a[[i]],a[[j]]}]],{i,1,2*n}],{j,1,2*n}]],2*n],{n,1,20}] (* _Geoffrey Critzer_, Apr 14 2013 *)
%o (PARI) a(n) = 3 * n * eulerphi(n); /* _Joerg Arndt_, Apr 14 2013 */
%Y Cf. A002618, A064279.
%K nonn
%O 1,1
%A Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Sep 28 2001
%E More terms from _Geoffrey Critzer_, Apr 14 2013
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