%I A036453
%S A036453 1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T A036453 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A036453 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A036453 a(n)=d[ d[ d[ d[ d[ n ] ] ] ] ], the 5th iterate of number-of-divisors 
               function with initial value of n.
%C A036453 The iterated d function rapidly converges to fixed point 2. In the 5-th 
               iterated d-sequence the first term different from the fixed point 
               2 appears at n=5040. The 6th and further iterated sequences have 
               very long initial segment of 2's. In the 6th one the first non-stationary 
               term is a(293318625600)=3. In such sequences any large value occurs 
               infinite many times and constructible.
%C A036453 Differs from A007395 for n=1, 5040, 7920, 8400, 9360, 10080, 10800 etc. 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 20 2008]
%F A036453 a[ n ]=Nest[ d, n, 5 ]
%e A036453 E.g. n=96 and its successive iterates are 12,6,4,3 and 2. The 5th term 
               is a(96)=2 is stationary(fixed).
%Y A036453 A000005, A015553, A036450, A036452.
%Y A036453 Sequence in context: A084100 A130130 A046698 this_sequence A040000 A007395 
               A055642
%Y A036453 Adjacent sequences: A036450 A036451 A036452 this_sequence A036454 A036455 
               A036456
%K A036453 nonn
%O A036453 1,2
%A A036453 Labos E. (labos(AT)ana.sote.hu)