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
Keywords
Examples
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.
Links
- Jonathan Frech, Table of n, a(n) for n = 1..100000
Programs
-
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}]