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A086858 Let f(n) be the inverse of the function g(x) = x^x. Then a(n) = floor(f(n)). 1
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.

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 October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)