%I
%S 1,94,5504,332106,24128092,2099467159,214910065296,25438034785805,
%T 3430631121407802,520643904835474202,87994213187313363255,
%U 16416338625038083857946,3355257076845892674934411,746397968687429806357762425,179698501514006236611711868382,46589028541465014633355926255885
%N a(2) = 1, and for n > 2 a(n) is the least k such that log(k) < k^(1/n) and log(k1) >= (k1)^(1/n).
%C A demonstration "that log x increases slower than any power of x. ... No matter how small you make a, the graph of log x is eventually flatter than the graph of x^a."
%D John Derbyshire, Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Joseph Henry Press, Washington, D.C., 2003, Page 72  75.
%F For n = 1, a(n) = 1. For n>=2, a(n) = ceiling(e^((n+1)*W1(1/(n+1)))) where W1(x) is the Lambert W function with branch 1.  _Wong Ching Yin_, Feb 26 2021
%t Table[ Floor[ FindRoot[ Log[x]^n == x, {x, 10^(2n)}, AccuracyGoal > 24, WorkingPrecision > 34][[1, 2]] + 1], {n, 2, 15}]
%K nonn
%O 2,2
%A _Robert G. Wilson v_, May 18 2003
%E a(14)a(16) from _Wong Ching Yin_, Feb 26 2021
%E Name clarified by _Pontus von BrÃ¶mssen_, Oct 11 2021
