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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
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 (list; graph; refs; listen; history; text; internal format)
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 PĂ©rez 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 * A285481 A282622 A102572

Adjacent sequences:  A036449 A036450 A036451 * A036453 A036454 A036455

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified April 25 13:31 EDT 2019. Contains 322461 sequences. (Running on oeis4.)