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 A058161 Number of labeled cyclic groups with a fixed identity. 6
 1, 1, 1, 3, 6, 60, 120, 1260, 6720, 90720, 362880, 9979200, 39916800, 1037836800, 10897286400, 163459296000, 1307674368000, 59281238016000, 355687428096000, 15205637551104000, 202741834014720000, 5109094217170944000, 51090942171709440000 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)