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%I #13 May 13 2018 02:09:21
%S 4,3,16,25,36,49,64,81,1000,1331,1728,2197,2744,3375,65536,83521,
%T 104976,130321,160000,194481,234256,6436343,7962624,9765625,11881376,
%U 14348907,17210368,20511149,729000000,887503681,1073741824,1291467969
%N Largest power of n not exceeding 2^n.
%H Harry J. Smith, <a href="/A060509/b060509.txt">Table of n, a(n) for n = 2..200</a>
%F a(n) = n^x, where x is floor(n/log_2(n)).
%e n=2: 4 <= 2^2 = 4;
%e n=3: 3 < 8 < 9;
%e n=4: 16 <= 16 < 32;
%e ...
%e n=20: 20^4 = 160000 < 1048576 = 2^20 < 3200000; etc.
%t Table[n^Floor[Log[n,2^n]],{n,2,40}] (* _Harvey P. Dale_, May 31 2014 *)
%o (PARI) { default(realprecision, 100); t=log(2); for (n=2, 200, x=floor(n*t/log(n)); write("b060509.txt", n, " ", n^x); ) } \\ _Harry J. Smith_, Jul 06 2009
%K nonn
%O 2,1
%A _Labos Elemer_, Apr 11 2001
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