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 A023142 Number of cycles of function f(x) = 10x mod n. 10
 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; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA 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, Apr 21 2003 EXAMPLE a(12) = 3 because the function 10x mod 12 has the three cycles (0),(1,10,4),(2,8). 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[10, n], {n, 100}] PROG (PARI) a(n)=n/=2^valuation(n, 2)*5^valuation(n, 5); sumdiv(n, d, eulerphi(d)/znorder(Mod(10, d))) \\ Charles R Greathouse IV, Apr 24 2013 CROSSREFS Cf. A000374, A023135-A023142. Sequence in context: A176514 A238559 A077196 * A225335 A229166 A143159 Adjacent sequences:  A023139 A023140 A023141 * A023143 A023144 A023145 KEYWORD nonn AUTHOR STATUS approved

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Last modified September 20 17:47 EDT 2020. Contains 337265 sequences. (Running on oeis4.)