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Search: id:A066508
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| A066508 |
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Floor[ sum 1..n (1/i)^(1/i)]. |
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+0
1
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| 1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 23, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 57, 58, 59, 60, 61, 62, 63, 64
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Floor(Sum[(1/i)^(1/i), {i=1 to n}]) = Floor(Sum[(i)^(-1/i), {i=1 to n}]).
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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Floor( H(n)^H(n) ) where H(n) is the n-th Harmonic number = A001008/A002805.
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EXAMPLE
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For a(5), 1^1 + (1/2)^(1/2) + (1/3)^(1/3) + (1/4)^(1/4) + (1/5)^(1/5) ~= 3.8323545. Therefore a(5) = 3.
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MATHEMATICA
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Table[ Floor[ Sum[ (1/i)^(1/i), {i, 1, n} ]], {n, 1, 75} ]
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PROGRAM
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(PARI) { s=0; for (n=1, 1000, s+=(1/n)^(1/n); write("b066508.txt", n, " ", floor(s)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 19 2010]
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CROSSREFS
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Cf. A067054.
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KEYWORD
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nonn,new
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 04 2002
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EXTENSIONS
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Example corrected by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 19 2010
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