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Search: id:A023142
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| A023142 |
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Number of cycles of function f(x) = 10x mod n. |
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+0
9
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| 1, 1, 3, 1, 1, 3, 2, 1, 9, 1, 6, 3, 3, 2, 3, 1, 2, 9, 2, 1, 6, 6, 2, 3, 1, 3, 15, 2, 2, 3, 3, 1, 18, 2, 2, 9, 13, 2, 9, 1, 9, 6, 3, 6, 9, 2, 2, 3, 3, 1, 6, 3, 5, 15, 6, 2, 6, 2, 2, 3, 2, 3, 18, 1, 3, 18, 3, 2, 6, 2, 3, 9, 10, 13, 3, 2, 17, 9, 7, 1, 21, 9, 3, 6, 2, 3, 6, 6, 3, 9, 16, 2, 9, 2, 2, 3, 2, 3, 54, 1, 26
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
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a(n) = Sum_{d|m} phi(d)/ord(10, d), where m is n with all factors of 2 and 5 removed. - T. D. Noe (noe(AT)sspectra.com), Apr 21 2003
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EXAMPLE
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a(12) = 3 because the function 10x mod 12 has the three cycles (0),(1,10,4),(2,8).
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MATHEMATICA
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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[10, n], {n, 100}]
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CROSSREFS
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Cf. A000374, A023135-A023142.
Sequence in context: A106749 A140216 A077196 this_sequence A033989 A099545 A132429
Adjacent sequences: A023139 A023140 A023141 this_sequence A023143 A023144 A023145
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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