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

1,2

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A010553, A036450, A036453.

Sequence in context: A211668 A255270 A211670 * A356852 A285481 A282622

Adjacent sequences: A036449 A036450 A036451 * A036453 A036454 A036455

Keyword

nonn

Author

Labos Elemer

Status

approved