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%I #19 Jan 03 2015 04:40:31
%S 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,
%T 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,2,
%U 2,2,2,3,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,3,2,2,2,2,2,3,2,2,2,2,2,2,2,2,2
%N a(n) = d(d(d(d(n)))), the 4th iterate of number-of-divisors function with initial value of n.
%C The iterated d function rapidly converges to fixed point 2. For k=4, the first n for which a(n)>2 is 60.
%H Enrique Pérez Herrero, <a href="/A036452/b036452.txt">Table of n, a(n) for n = 1..2000</a>
%F a(n) = d(d(d(d(n)))).
%e E.g., n=96 and its successive iterates are 12,6,4,3 and 2. The 4th term is a(96)=3.
%t f[n_]:=DivisorSigma[0,n]; Table[Nest[f,n,4], {n,100}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 10 2010 *)
%o (PARI) a(n)=my(d=numdiv);d(d(d(d(n)))) \\ _Charles R Greathouse IV_, Apr 07 2012
%Y Cf. A000005, A010553, A036450, A036453.
%K nonn
%O 1,2
%A _Labos Elemer_