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 A086858 Let f(n) be the inverse of the function g(x) = x^x. Then a(n) = floor(f(n)). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) is the value of x that solves the equation x^x = n, truncated to an integer. LINKS Table of n, a(n) for n=1..105. FORMULA a(n) = floor(g^-1(n)) where g(x) = x^x. EXAMPLE a(32)=3 because the solution to the equation x^x = 32 is x = 3.080448349..., and floor(3.080448349...) = 3. MATHEMATICA f[n_] := Floor[ N[ Log[n]/ProductLog[Log[ n]]]]; Join[{1}, Table[ f[n], {n, 2, 105}]] (* Robert G. Wilson v, Oct 21 2005 *) CROSSREFS Cf. A000312, A095703. Sequence in context: A105519 A111891 A296076 * A111892 A108248 A087104 Adjacent sequences: A086855 A086856 A086857 * A086859 A086860 A086861 KEYWORD easy,nonn AUTHOR Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Sep 16 2003 EXTENSIONS Edited by Jon E. Schoenfield, Sep 09 2017 STATUS approved

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Last modified December 5 00:23 EST 2023. Contains 367565 sequences. (Running on oeis4.)