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A086858
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Let f(n) be the inverse of the function g(x) = x^x. Then a(n) = floor(f(n)).
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2
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1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET
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1,4
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COMMENTS
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a(n) is the value of x that solves the equation x^x = n, truncated to an integer.
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LINKS
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FORMULA
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a(n) = floor(g^-1(n)) where g(x) = x^x.
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EXAMPLE
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a(32)=3 because the solution to the equation x^x = 32 is x = 3.080448349..., and floor(3.080448349...) = 3.
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MATHEMATICA
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f[n_] := Floor[ N[ Log[n]/ProductLog[Log[ n]]]]; Join[{1}, Table[ f[n], {n, 2, 105}]] (* Robert G. Wilson v, Oct 21 2005 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Sep 16 2003
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EXTENSIONS
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STATUS
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approved
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