

A036459


Number of iterations required to reach stationary value when repeatedly applying d, the number of divisors function (A000005).


24



0, 0, 1, 2, 1, 3, 1, 3, 2, 3, 1, 4, 1, 3, 3, 2, 1, 4, 1, 4, 3, 3, 1, 4, 2, 3, 3, 4, 1, 4, 1, 4, 3, 3, 3, 3, 1, 3, 3, 4, 1, 4, 1, 4, 4, 3, 1, 4, 2, 4, 3, 4, 1, 4, 3, 4, 3, 3, 1, 5, 1, 3, 4, 2, 3, 4, 1, 4, 3, 4, 1, 5, 1, 3, 4, 4, 3, 4, 1, 4, 2, 3, 1, 5, 3, 3, 3, 4, 1, 5, 3, 4, 3, 3, 3, 5, 1, 4, 4
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OFFSET

1,4


COMMENTS

Iterating d for n, the prestationary prime and finally the fixed value of 2 is reached in different number of steps; a(n) is the number of required iterations.
Each value n > 0 occurs an infinite number of times. For positions of first occurrences of n, see A251483.  Ivan Neretin, Mar 29 2015


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = a(d(n)) + 1 if n > 2.
a(n) = 1 iff n is an odd prime.


EXAMPLE

If n=8, then d(8)=4, d(d(8))=3, d(d(d(8)))=2, which means that a(n)=3. In terms of the number of steps required for convergence, the distance of n from the dequilibrium is expressed by a(n). A similar method is used in A018194.


MATHEMATICA

Table[ Length[ FixedPointList[ DivisorSigma[0, # ] &, n]]  2, {n, 105}] (* Robert G. Wilson v, Mar 11 2005 *)


PROG

(PARI) for(x = 1, 150, for(a=0, 15, if(a==0, d=x, if(d<3, print(a1), d=numdiv(d) )) ))
(PARI) a(n)=my(t); while(n>2, n=numdiv(n); t++); t \\ Charles R Greathouse IV, Apr 07 2012


CROSSREFS

Equals A060937  1. Cf. A007624, A036450, A046452, A036453, A036455, A030630.
Sequence in context: A191350 A329616 A304795 * A294926 A079167 A304793
Adjacent sequences: A036456 A036457 A036458 * A036460 A036461 A036462


KEYWORD

nonn


AUTHOR

Labos Elemer


STATUS

approved



