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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.
11
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 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
KEYWORD
nonn
AUTHOR
STATUS
approved