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A063947
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Infinitary harmonic numbers: harmonic mean of infinitary divisors is an integer.
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17
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1, 6, 45, 60, 90, 270, 420, 630, 2970, 5460, 8190, 9100, 15925, 27300, 36720, 40950, 46494, 54600, 81900, 95550, 136500, 163800, 172900, 204750, 232470, 245700, 257040, 409500, 464940, 491400, 646425, 716625, 790398, 791700, 819000, 900900
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OFFSET
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1,2
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LINKS
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P. Hagis, Jr. and G. L. Cohen, Infinitary harmonic numbers, Bull. Australian math. Soc., 41 (1990), 151-158 (Math. Rev. 91d:11001) (asymptotics).
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MATHEMATICA
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bitty[ k_ ] := Union[ Flatten[ Outer[ Plus, Sequence @@ ({0, #} & /@ Union[ (2^Range[ 0, Floor[ Log[ 2, k ] ] ] ) Reverse[ IntegerDigits[ k, 2 ] ] ] ) ] ] ]; 1 + Flatten[ Position[ Table[ (Length[ # ] /(Plus @@ (1/#)) &)@ (Apply[ Times, (First[ it ] ^ (# /. z -> List)) ] & /@ Flatten[ Outer[ z, Sequence @@ (bitty /@ Last[ it = Transpose[ FactorInteger[ k ] ] ] ), 1 ] ]), {k, 2, 2^22 + 1} ], _Integer ] ] (* Robert G. Wilson v, Sep 04 2001 *)
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PROG
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(Haskell)
import Data.Ratio (denominator)
import Data.List (genericLength)
a063947 n = a063947_list !! (n-1)
a063947_list = filter ((== 1) . denominator . hm . a077609_row) [1..]
where hm xs = genericLength xs / sum (map (recip . fromIntegral) xs)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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