

A087891


Number of nonsquarefree terms in 3x+1 trajectory started at n.


1



0, 0, 3, 1, 3, 3, 6, 2, 8, 3, 6, 4, 5, 6, 7, 3, 6, 9, 8, 4, 5, 6, 7, 5, 10, 5, 38, 7, 8, 7, 36, 4, 12, 6, 7, 10, 9, 8, 12, 5, 37, 5, 13, 7, 9, 7, 36, 6, 11, 11, 10, 6, 7, 39, 40, 8, 14, 8, 12, 8, 9, 36, 36, 5, 13, 12, 11, 7, 8, 7, 36, 11, 41, 9, 9, 9, 10, 12, 13, 6, 11, 37, 40, 6, 7, 13, 12, 8, 12
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..89.


EXAMPLE

n=61: trajectory = {61,184,92,46,23,70,35,...,20,10,5,16,8,4,2,1},
nonsquarefree terms = {184,92,160,80,40,20,16,8,4}, so a(61)=9.


MATHEMATICA

c[x_] := (1Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1); c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], 1] lf[x_] := Length[fpl[x]] Table[Count[Table[MoebiusMu[Part[fpl[w], j]], {j, 1, lf[w]}], 0], {w, 1, 256}]


CROSSREFS

Sequence in context: A165027 A078555 A259286 * A005885 A205145 A061892
Adjacent sequences: A087888 A087889 A087890 * A087892 A087893 A087894


KEYWORD

nonn


AUTHOR

Labos Elemer, Oct 02 2003


STATUS

approved



