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%I #12 Apr 21 2023 06:30:07
%S 3,2,1,4,3,6,5,5,5,4,3,4,3,3,3,5,4,3,2,8,4,3,2,7,11,4,8,10,9,8,7,4,6,
%T 4,3,12,11,12,10,11,10,5,4,10,9,4,3,6,9,9,12,6,5,9,11,5,2,11,10,11,10,
%U 11,6,8,11,10,9,10,11,9,8,14,13,9,5,10,13,5,4
%N For x=n, iterate the map x -> Product_{k is a prime dividing x} (k + (multiplicity of k)), a(n) is the number of steps to see a repeated term for the first time.
%C It appears that all n end in one of the orbits (6,12,16) or (20,24) or one of the fixed points 4, 90, 120, verified to n=10^8.
%H Lars Blomberg, <a href="/A299352/b299352.txt">Table of n, a(n) for n = 2..10000</a>
%e For n=2: 2=2^1 -> (2+1)=3=3^1 -> (3+1)=4=2^2 -> (2+2)=4; 4 is repeated so a(2)=3.
%e For n=12: 12=2^2*3^1 -> (2+2)*(3+1)=16=2^4 -> (2+4)=6=2^1*3^1 -> (2+1)*(3+1)=12; 12 is repeated so a(12)=3.
%Y Cf. A008473 (the map), A299351.
%K nonn
%O 2,1
%A _Lars Blomberg_, Feb 07 2018
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