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A055980
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a(n) = floor(Sum_{i=1..n} 1/i).
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10
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1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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COMMENTS
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If we choose at random (uniformly) a permutation in the symmetric group S_n then a(n) is the expected number of cycles (rounded down) in the cycle decomposition of the permutation. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Oct 17 2001
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LINKS
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FORMULA
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a(n) ~ log(n) - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 25 2001
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MATHEMATICA
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PROG
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(Haskell)
import Data.Ratio ((%), denominator)
a055980 = floor . sum . map (1 %) . enumFromTo 1
a055980_list = map floor $ scanl1 (+) $ map (1 %) [1..]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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