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Numbers n such that A033493(n)/n is an integer.
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%I #22 Mar 13 2015 05:00:41

%S 1,57,847,1694,3039,3388,3479,6078,6776,6958,13916,27832,55664,111328,

%T 236107,246721,311257,493442,622514,986884,1245028,1328233,1973768,

%U 2052521,2490056,2656466,3947536,4105042,4980112,8210084

%N Numbers n such that A033493(n)/n is an integer.

%C If A033493(n)/n = M is even, then 2*n is a member of the sequence and A033493(2*n)/(2*n) = M/2 + 1.

%C a(31) > 10^7. - _Derek Orr_, Mar 12 2015

%C Sum of reciprocals seems to converge quickly to 1.0208... - _Derek Orr_, Mar 12 2015

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CollatzProblem.html">CollatzProblem</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">Collatz conjecture</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%t a033493[n_] := Block[{f}, f[1] = 1; f[x_Integer?OddQ] := 3 x + 1; f[x_Integer?EvenQ] := x/2; -1 + Plus @@ FixedPointList[f, n]]; Select[Range[10^5], IntegerQ[a033493[#]/#] &] (* _Michael De Vlieger_, Feb 09 2015, after _Alonso del Arte_ at A033493 *)

%o (PARI) Tsum(n)=s=n;while(n!=1,if(n==Mod(0,2),n=n/2;s+=n);if(n==Mod(1,2)&&n!=1,n=3*n+1;s+=n));s

%o for(n=1,10^6,if(type(Tsum(n)/n)=="t_INT",print1(n,", ")))

%Y Cf. A033493.

%K nonn,more,hard

%O 1,2

%A _Derek Orr_, Feb 07 2015