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%I #17 May 16 2013 16:57:13
%S 1,3,617,7,171,219,766329,15,1061683,179,102151,677,497,785777,
%T 10380059,31,8861,360377,60226515,183,2731,103919,3339321,229,
%U 1548244271,505,129481899470258402665619129356105706380861444925035330406812603986229803685477,113643
%N Numerators of the sums of reciprocals of the Collatz (3x+1) sequence beginning with n and stopping at 1.
%C If the sum of the reciprocals of a Collatz sequence is bounded, there are no cycles other than 4,2,1.
%C a(n) = numerator of sum (1/A070165(n,k): k = 1..A006577(n)). - _Reinhard Zumkeller_, May 16 2013
%H Reinhard Zumkeller, <a href="/A225761/b225761.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e For n=9 the Collatz sequence is {9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 4, 2, 1}. So the sum of the reciprocals is 1/9 + 1/28 + 1/14 + 1/7 + 1/22 + 1/11 + ... + 1/4 + 1/2 + 1/1 = 1061683/350064, whose numerator is 1061683.
%t Table[Numerator[Total[1/Collatz[n]]], {n, 40}] (* _T. D. Noe_, May 15 2013 *)
%o (Haskell)
%o import Data.Ratio (numerator)
%o a225761 = numerator . sum . map (recip . fromIntegral) . a070165_row
%o -- _Reinhard Zumkeller_, May 16 2013
%Y Cf. A087226, A225784 (denominators).
%Y Cf. A225843.
%K nonn
%O 1,2
%A _Nico Brown_, May 14 2013
%E Extended by _T. D. Noe_, May 15 2013
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