OFFSET
1,2
COMMENTS
The iterated d function rapidly converges to the fixed point 2.
From N. J. A. Sloane, Jun 02 2014: (Start)
The fourth iterate begins as follows:
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, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ... . (End)
REFERENCES
S. Ramanujan, Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962, p. 128. - N. J. A. Sloane, Jun 02 2014
LINKS
Enrique Pérez Herrero, Table of n, a(n) for n = 1..2000
R. Bellman and H. N. Shapiro, On a problem in additive number theory, Annals Math., 49 (1948), 333-340.
EXAMPLE
n = 5040, d(5040) = 60, d(d(5040)) = d(60) = 12 and a(5040) = d(12) = 6.
MATHEMATICA
f[n_]:=Length[Divisors[n]]; Table[Nest[f, n, 3], {n, 6!}] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2010 *)
PROG
(PARI) a(n)=numdiv(numdiv(numdiv(n))) \\ Charles R Greathouse IV, Nov 16 2022
(Python)
from sympy import divisor_count
def A036450(n): return divisor_count(divisor_count(divisor_count(n))) # Chai Wah Wu, Nov 17 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved