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A005424
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Smallest number that requires n iterations of the bi-unitary totient function (A116550) to reach 1.
(Formerly M0530)
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5
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2, 3, 4, 5, 8, 9, 13, 16, 17, 24, 25, 35, 44, 63, 64, 91, 97, 128, 193, 221, 259, 324, 353, 391, 477, 702, 929, 1188, 1269, 1589, 1613, 2017, 2309, 2623, 3397, 4064, 4781, 5468, 6515, 6887, 9213, 12286, 12887, 14009, 16564, 16897, 17803, 30428, 36256
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OFFSET
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1,1
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COMMENTS
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Let p(n) = number of unitary divisors k of n, k<n, that are relatively prime to n. Let p_1(n) = p(n), p_r(n) = p(p_{r-1}(n)). Sequence gives minimal r such that p_r(n)=1.
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REFERENCES
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M. Lal, H. Wareham and R. Mifflin, Iterates of the bi-unitary totient function, Utilitas Math., 10 (1976), 347-350.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MAPLE
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L := [seq(0, i=0..100)] ;
for n from 1 do
if itr < nops(L) then
if op(itr, L) = 0 then
L := subsop(itr=n, L) ;
print(L) ;
end if;
end if;
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MATHEMATICA
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A116550[1] = 1; A116550[n_] := With[{pp = Power @@@ FactorInteger[n]}, Count[Range[n], m_ /; Intersection[pp, Power @@@ FactorInteger[m]] == {}]]; A225320[n_] := A225320[n] = If[n == 1, 0, 1+A225320[A116550[n]]]; L = Array[0&, 100]; For[n = 1, n <= 40000, n++, itr = A225320[n]; If[itr < Length[L], If[L[[itr]] == 0, L = ReplacePart[L, itr -> n]; Print[Select[L, Positive] // Last]]]]; Select[L, Positive] (* Jean-François Alcover, Jan 13 2014, after R. J. Mathar *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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