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Number of steps to get from n to 1 by process of replacing with the Carmichael function lambda if the result is odd, or dividing by 2 if even.
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%I #7 Mar 30 2017 22:02:13

%S 0,1,2,2,3,3,4,3,4,4,5,4,5,5,3,4,5,5,6,5,4,6,7,5,6,6,6,6,7,4,5,5,5,6,

%T 5,6,7,7,5,6,7,5,6,7,5,8,9,6,6,7,5,7,8,7,6,7,6,8,9,5,6,6,4,6,5,6,7,7,

%U 7,6,7,7,8,8,6,8,5,6,7,7,8,8,9,6,5,7,7

%N Number of steps to get from n to 1 by process of replacing with the Carmichael function lambda if the result is odd, or dividing by 2 if even.

%e a(19)= 6 because 19 -> lambda(19)= 18 -> 9 -> lambda(9)= 6 -> 3 -> lambda(3)= 2 -> 1, hence the trajectory {19 -> 18 -> 9 -> 6 -> 3 -> 2 -> 1} with 6 iterations.

%t f[n_]:=Module[{a=n,k=0},While[a!=1,k++;If[EvenQ[a],a=a/2,a=CarmichaelLambda[a]]];k];Table[f[n],{n,1,150}]

%Y Cf. A002322.

%K nonn,easy

%O 1,3

%A _Michel Lagneau_, Jul 07 2015