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

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

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.

a(n) ~ log n/log log n. - Charles R Greathouse IV, Nov 29 2024

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 *)

Prog

(PARI) a(n)=exp(lambertw(log(x)))\1 \\ Charles R Greathouse IV, Nov 29 2024

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