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Numbers k such that the number of steps to reach 1 in '3x+1' problem equals tau(k), the number of divisors of k.
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%I #23 Oct 20 2019 22:03:33

%S 40,42,96,180,280,1664,1704,1932,1960,2184,2304,2310,4816,4928,7252,

%T 9360,9792,12888,12896,13338,13720,14256,15792,16240,17408,17940,

%U 17952,18096,20000,20016,21200,21450,25080,25600,27136,28980,30016,31808,34048,34240,34320,34368,35028,36576,36652,37332,38088,39936,45056,47880

%N Numbers k such that the number of steps to reach 1 in '3x+1' problem equals tau(k), the number of divisors of k.

%C Are all terms even?

%C Numbers k such that A006577(k) = A000005(k).

%C Not all terms are even. In the first 200 terms, three are odd: 82485, 91665, and 337365. - _Harvey P. Dale_, Feb 16 2014

%H Harvey P. Dale, <a href="/A070980/b070980.txt">Table of n, a(n) for n = 1..200</a>

%t nsQ[n_]:=Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#!=1&]]-1 == DivisorSigma[ 0,n]; Select[Range[50000],nsQ] (* _Harvey P. Dale_, Feb 15 2014 *)

%o (PARI) for(n=1,40000,s=n; t=0; while(s!=1,t++; if(s%2==0,s=s/2,s=3*s+1); if(s==if(numdiv(n)-t,0,1),print1(n,","); ); ))

%K nonn

%O 1,1

%A _Benoit Cloitre_ and Boris Gourevitch (boris(AT)pi314.net), May 17 2002

%E Corrected and extended by _Harvey P. Dale_, Feb 15 2014