A036458 For all n, if d is recursively applied to a(n) exactly 6 times then the fixed point of d-iteration is just reached.

5040, 7920, 8400, 9360, 10080, 10800, 11088, 11340, 11760, 12240, 12600, 12960, 13104, 13200, 13680, 13860, 15600, 15840, 16200, 16380, 16560, 16800, 17136, 17640, 17820, 18000, 18144, 18720, 18900, 19152, 19440, 19800, 20160, 20400, 20592, 20880, 21060, 21168

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

Observe that the values giving stationary value in 6 steps are rather large.

"d" in the definition refers to the number of divisors of n. - Harvey P. Dale, Mar 06 2015

Examples

			a(1)=5040 and the nested d functions are 60,12,6,4,3 and the 6th is 2. a(5)=10080 and iterating d with 10080 initial value, after 6 iterations the convergence takes place through 72,12,6,4,3 transients, i.e., 2 is reached on the 6th step.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A036457, A036459.

Programs

Mathematica

draQ[n_]:=Length[FixedPointList[DivisorSigma[0,#]&,n,7]]==8; Select[ Range[ 21000],draQ] (* Harvey P. Dale, Mar 06 2015 *)

PARI

is(n)=for(i=1,5,n=numdiv(n); if(n<3, return(0))); numdiv(n)==2 \\ Charles R Greathouse IV, Sep 17 2015

Formula

A036459(a(n)) = 6. - Ivan Neretin, Jan 25 2016