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A023141
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Number of cycles of function f(x) = 9x mod n.
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1
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1, 2, 1, 4, 3, 2, 3, 8, 1, 6, 3, 4, 5, 6, 3, 12, 3, 2, 3, 12, 3, 6, 3, 8, 5, 10, 1, 12, 3, 6, 3, 16, 3, 6, 9, 4, 5, 6, 5, 24, 11, 6, 3, 12, 3, 6, 3, 12, 5, 10, 3, 20, 3, 2, 9, 24, 3, 6, 3, 12, 13, 6, 3, 20, 15, 6, 7, 12, 3, 18, 3, 8, 13, 10, 5, 12, 9, 10, 3, 44, 1, 22, 3, 12, 13, 6, 3, 24, 3, 6, 31, 12, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
| a(n) = Sum_{d|m} phi(d)/ord(9, d), where m is n with all factors of 3 removed. - T. D. Noe (noe(AT)sspectra.com), Apr 21 2003
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EXAMPLE
| a(12) = 4 because the function 9x mod 12 has the four cycles (0),(3),(1,9),(2,6).
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MATHEMATICA
| CountFactors[p_, n_] := Module[{sum=0, m=n, d, f, i, ps, j}, ps=Transpose[FactorInteger[p]][[1]]; Do[While[Mod[m, ps[[j]]]==0, m/=ps[[j]]], {j, Length[ps]}]; d=Divisors[m]; Do[f=d[[i]]; sum+=EulerPhi[f]/MultiplicativeOrder[p, f], {i, Length[d]}]; sum]; Table[CountFactors[9, n], {n, 100}]
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CROSSREFS
| Cf. A000374, A023135-A023142.
Sequence in context: A183201 A082467 A106407 * A072650 A082497 A065620
Adjacent sequences: A023138 A023139 A023140 * A023142 A023143 A023144
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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