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 A214003 Number of degree-n permutations of prime order. 3
 0, 1, 5, 17, 69, 299, 1805, 9099, 37331, 205559, 4853529, 49841615, 789513659, 9021065871, 70737031469, 420565124399, 22959075244095, 385032305178719, 10010973102879761, 152163983393187399, 1498273284120348539, 15639918041915598815, 1296204202723400597109 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Stephen A. Silver, Table of n, a(n) for n = 1..451 FORMULA a(n) = Sum_{p prime} A057731(n,p). E.g.f.: exp(x)*Sum_{p in Primes} exp(x^p/p)-1. - Geoffrey Critzer, Nov 08 2015 EXAMPLE The symmetric group S_5 has 25 elements of order 2, 20 elements of order 3, and 24 elements of order 5. All other elements are of nonprime order (1, 4, or 6), so a(5) = 25 + 20 + 24 = 69. MAPLE b:= proc(n, p) option remember;       `if`(n add(b(n, ithprime(i)), i=1..numtheory[pi](n)): seq(a(n), n=1..30);  # Alois P. Heinz, Feb 16 2013 MATHEMATICA f[list_] :=Total[list]!/Apply[Times, list]/Apply[Times, Map[Length, Split[list]]!]; Table[Total[Map[f, Select[Partitions[n], PrimeQ[Apply[LCM, #]] &]]], {n, 1, 23}] (* Geoffrey Critzer, Nov 08 2015 *) CROSSREFS Cf. A001189, A001471, A057731, A059593, A153760, A153761, A186202. Sequence in context: A149706 A273763 A149707 * A249015 A273852 A146511 Adjacent sequences:  A214000 A214001 A214002 * A214004 A214005 A214006 KEYWORD nonn AUTHOR Stephen A. Silver, Feb 15 2013 STATUS approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)