A058161 - OEIS

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

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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 *)