This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A086858 #15 Nov 29 2024 09:58:39
%S A086858 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,
%T A086858 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,
%U A086858 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
%N A086858 Let f(n) be the inverse of the function g(x) = x^x. Then a(n) = floor(f(n)).
%C A086858 a(n) is the value of x that solves the equation x^x = n, truncated to an integer.
%F A086858 a(n) = floor(g^-1(n)) where g(x) = x^x.
%F A086858 a(n) ~ log n/log log n. - _Charles R Greathouse IV_, Nov 29 2024
%e A086858 a(32)=3 because the solution to the equation x^x = 32 is x = 3.080448349..., and floor(3.080448349...) = 3.
%t A086858 f[n_] := Floor[ N[ Log[n]/ProductLog[Log[ n]]]]; Join[{1}, Table[ f[n], {n, 2, 105}]] (* _Robert G. Wilson v_, Oct 21 2005 *)
%o A086858 (PARI) a(n)=exp(lambertw(log(x)))\1 \\ _Charles R Greathouse IV_, Nov 29 2024
%Y A086858 Cf. A000312, A095703.
%K A086858 easy,nonn
%O A086858 1,4
%A A086858 Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Sep 16 2003
%E A086858 Edited by _Jon E. Schoenfield_, Sep 09 2017