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A058161
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Number of labeled cyclic groups with a fixed identity.
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7
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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
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1,4
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COMMENTS
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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
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REFERENCES
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J. L. Lagrange, Oeuvres, Vol. III Paris 1869.
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LINKS
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FORMULA
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a(n) = (n-1)!/phi(n).
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EXAMPLE
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a(4)=3 because we have: <(1234)> = <(1432)>, <(1243)> = <(1342)>, <(1324)> = <(1423)>. - Geoffrey Critzer, Sep 07 2015
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MATHEMATICA
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Table[n!/(n EulerPhi[n]), {n, 1, 20}] (* Artur Jasinski, Jan 22 2008 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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