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

1,4

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

References

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

Links

Table of n, a(n) for n=1..23.

Index entries for sequences related to groups

Formula

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

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

Example

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

Mathematica

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

Crossrefs

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

Cf. A058162, A058163.

Cf. A002618.

Sequence in context: A067610 A067609 A012473 * A012877 A103066 A145887

Adjacent sequences: A058158 A058159 A058160 * A058162 A058163 A058164

Keyword

nonn

Author

Christian G. Bower, Nov 14 2000

Status

approved