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

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, 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, 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

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

The iterated d function rapidly converges to fixed point 2. For k=4, the first n for which a(n)>2 is 60.

Examples

			E.g., n=96 and its successive iterates are 12,6,4,3 and 2. The 4th term is a(96)=3.
		

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000005, A010553, A036450, A036453.

Programs

Mathematica

f[n_]:=DivisorSigma[0,n]; Table[Nest[f,n,4], {n,100}] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2010 *)

PARI

a(n)=my(d=numdiv);d(d(d(d(n)))) \\ Charles R Greathouse IV, Apr 07 2012

Formula

a(n) = d(d(d(d(n)))).