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A225784
Denominators of the sum of the reciprocals of the Collatz (3x+1) sequence beginning at n.
5
1, 2, 240, 4, 80, 80, 272272, 8, 350064, 80, 38896, 240, 208, 272272, 4095840, 16, 3536, 116688, 21431696, 80, 1344, 38896, 1365280, 80, 535792400, 208, 44841486948146266934850832405421294927083491752830032389039800908293040266400, 38896, 1127984, 1365280
OFFSET
1,2
COMMENTS
If the sum of the reciprocals of a Collatz sequence is bounded, there are no Collatz cycles other than 4,2,1,4,2,1,...
a(n) = denominator of Sum_{k = 1..A006577(n)} 1/A070165(n,k). - Reinhard Zumkeller, May 16 2013
EXAMPLE
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 denominator is 350064.
MATHEMATICA
Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[Denominator[Total[1/Collatz[n]]], {n, 40}] (* T. D. Noe, May 15 2013 *)
PROG
(Haskell)
import Data.Ratio (denominator)
a225784 = denominator . sum . map (recip . fromIntegral) . a070165_row
-- Reinhard Zumkeller, May 16 2013
CROSSREFS
Cf. A225761 (numerators), A087226.
Cf. A225843.
Sequence in context: A013477 A013473 A212839 * A087226 A217972 A071967
KEYWORD
nonn
AUTHOR
Nico Brown, May 15 2013
EXTENSIONS
Extended by T. D. Noe, May 15 2013
STATUS
approved