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%I #14 Apr 04 2021 13:02:39
%S 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,
%T 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,
%U 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
%N Number of nonsquarefree terms in 3x+1 trajectory started at n.
%H Jonathan Frech, <a href="/A087891/b087891.txt">Table of n, a(n) for n = 1..100000</a>
%e n=61: trajectory = {61,184,92,46,23,70,35,...,20,10,5,16,8,4,2,1},
%e nonsquarefree terms = {184,92,160,80,40,20,16,8,4}, so a(61)=9.
%t 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}]
%K nonn
%O 1,3
%A _Labos Elemer_, Oct 02 2003
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