A058161 Number of labeled cyclic groups with a fixed identity.

1, 1, 1, 3, 6, 60, 120, 1260, 6720, 90720, 362880, 9979200, 39916800, 1037836800, 10897286400, 163459296000, 1307674368000, 59281238016000, 355687428096000, 15205637551104000, 202741834014720000, 5109094217170944000, 51090942171709440000

Offset: 1

Author

Christian G. Bower, Nov 14 2000

Keywords

• nonn

Comments

Degree of Lagrange resolvent of polynomial of n-th degree. Equals degree of symmetric group of order n divided by order of metacyclic group of order n. - Artur Jasinski, Jan 22 2008

Examples

			a(4)=3 because we have: <(1234)> = <(1432)>,  <(1243)> = <(1342)>,  <(1324)> = <(1423)>. - _Geoffrey Critzer_, Sep 07 2015
		

References

• J. L. Lagrange, Oeuvres, Vol. III Paris 1869.

Links

• Index entries for sequences related to groups

Crossrefs

a(n) = A000142(n-1)/A000010(n) = A034381(n)/n.

Cf. A058162, A058163.

Cf. A002618.

Programs

Mathematica

Table[n!/(n EulerPhi[n]), {n, 1, 20}] (* Artur Jasinski, Jan 22 2008 *)

Formula

a(n) = (n-1)!/phi(n).

a(n) = n!/A002618(n) - Artur Jasinski, Jan 22 2008