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A036452 a(n) = d(d(d(d(n)))), the 4th iterate of number-of-divisors function with initial value of n. 8

%I

%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 PĂ©rez 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_

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Last modified February 18 09:39 EST 2020. Contains 332011 sequences. (Running on oeis4.)