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A036457 Numbers k for which exactly 5 applications of A000005 are needed to reach 2.

%I A036457 #35 Jan 03 2025 20:52:50
%S A036457 60,72,84,90,96,108,126,132,140,150,156,160,180,198,200,204,220,224,
%T A036457 228,234,240,252,260,276,288,294,300,306,308,315,336,340,342,348,350,
%U A036457 352,360,364,372,380,392,396,414,416,420,432,444,450,460,468,476,480
%N A036457 Numbers k for which exactly 5 applications of A000005 are needed to reach 2.
%C A036457 Subsequences include A030630 (numbers with 12 divisors), A030636 (numbers with 18 divisors), A030638 (numbers with 20 divisors), A137491 (numbers with 28 divisors), etc. [edited by _Jon E. Schoenfield_, May 12 2018]
%H A036457 Robert Israel, <a href="/A036457/b036457.txt">Table of n, a(n) for n = 1..10000</a>
%F A036457 d(d(d(d(d(a(n)))))) = 2 for all n.
%F A036457 A036459(a(n)) = 5. - _Ivan Neretin_, Jan 25 2016
%e A036457 a(13)=180; the successive iterates are 18, 6, 4, 3, and finally the 5th is 2;
%e A036457 a(3)=84; divisor numbers are 12, 6, 4, 3, and 2.
%p A036457 A036459:= proc(n) option remember;
%p A036457   if n <= 2 then 0 else 1 + procname(numtheory:-tau(n)) fi
%p A036457 end proc:
%p A036457 select(A036459 = 5, [$1..1000]); # _Robert Israel_, Jan 25 2016
%t A036457 Select[Range@ 480, Last@ # == 2 && #[[5]] != 2 &@ NestList[DivisorSigma[0, #] &, #, 5] &] (* _Michael De Vlieger_, Jan 26 2016 *)
%o A036457 (PARI) is(n)=for(i=1,4,n=numdiv(n); if(n<3, return(0))); numdiv(n)==2 \\ _Charles R Greathouse IV_, Sep 17 2015
%Y A036457 Cf. A000005, A007624, A036450, A036452, A036453, A036455, A030630.
%K A036457 nonn
%O A036457 1,1
%A A036457 _Labos Elemer_
%E A036457 New name from _Robert Israel_, Jan 25 2016