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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.

%I A036458 #32 Jun 11 2022 18:41:42
%S A036458 5040,7920,8400,9360,10080,10800,11088,11340,11760,12240,12600,12960,
%T A036458 13104,13200,13680,13860,15600,15840,16200,16380,16560,16800,17136,
%U A036458 17640,17820,18000,18144,18720,18900,19152,19440,19800,20160,20400,20592,20880,21060,21168
%N 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.
%C A036458 Observe that the values giving stationary value in 6 steps are rather large.
%C A036458 "d" in the definition refers to the number of divisors of n. - _Harvey P. Dale_, Mar 06 2015
%H A036458 Amiram Eldar, <a href="/A036458/b036458.txt">Table of n, a(n) for n = 1..10000</a>
%F A036458 A036459(a(n)) = 6. - _Ivan Neretin_, Jan 25 2016
%e A036458 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.
%t A036458 draQ[n_]:=Length[FixedPointList[DivisorSigma[0,#]&,n,7]]==8; Select[ Range[ 21000],draQ] (* _Harvey P. Dale_, Mar 06 2015 *)
%o A036458 (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
%Y A036458 Cf. A000005, A036457, A036459.
%K A036458 nonn
%O A036458 1,1
%A A036458 _Labos Elemer_