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Search: id:A063947
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| A063947 |
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Infinitary harmonic numbers: harmonic mean of infinitary divisors is an integer. |
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+0
1
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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
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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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 ] ]
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CROSSREFS
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Cf. A037445, A049417.
Sequence in context: A065783 A077672 A119202 this_sequence A006086 A131513 A123141
Adjacent sequences: A063944 A063945 A063946 this_sequence A063948 A063949 A063950
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KEYWORD
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nonn,nice
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AUTHOR
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wouter.meeussen(AT)pandora.be, Sep 03 2001
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EXTENSIONS
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More terms from David W. Wilson, Sep 04, 2001. Mma program from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 04 2001.
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