A087891 Number of nonsquarefree terms in 3x+1 trajectory started at n.

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

Offset

1,3

Links

Jonathan Frech, Table of n, a(n) for n = 1..100000

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_] := (1-Mod[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: A342341 A078555 A259286 * A005885 A333334 A205145

Adjacent sequences: A087888 A087889 A087890 * A087892 A087893 A087894

Keyword

nonn

Author

Labos Elemer, Oct 02 2003

Status

approved