A064400 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.

3, 6, 18, 24, 60, 36, 126, 96, 162, 120, 330, 144, 468, 252, 360, 384, 816, 324, 1026, 480, 756, 660, 1518, 576, 1500, 936, 1458, 1008, 2436, 720, 2790, 1536, 1980, 1632, 2520, 1296, 3996, 2052, 2808, 1920, 4920, 1512, 5418, 2640, 3240, 3036, 6486, 2304, 6174, 3000, 4896, 3744, 8268

Offset

1,1

Links

Kenneth G. Hawes, Table of n, a(n) for n = 1..10000

Formula

a(n) = 3 * A002618(n) = 3 * n * phi(n).

Mathematica

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 *)

Prog

(PARI) a(n) = 3 * n * eulerphi(n); /* Joerg Arndt, Apr 14 2013 */

Crossrefs

Cf. A002618, A064279.

Sequence in context: A074370 A174101 A088339 * A352786 A117863 A103100

Adjacent sequences: A064397 A064398 A064399 * A064401 A064402 A064403

Keyword

nonn

Author

Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Sep 28 2001

Extensions

More terms from Geoffrey Critzer, Apr 14 2013

Status

approved