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A060509
Largest power of n not exceeding 2^n.
1
4, 3, 16, 25, 36, 49, 64, 81, 1000, 1331, 1728, 2197, 2744, 3375, 65536, 83521, 104976, 130321, 160000, 194481, 234256, 6436343, 7962624, 9765625, 11881376, 14348907, 17210368, 20511149, 729000000, 887503681, 1073741824, 1291467969
OFFSET
2,1
LINKS
FORMULA
a(n) = n^x, where x is floor(n/log_2(n)).
EXAMPLE
n=2: 4 <= 2^2 = 4;
n=3: 3 < 8 < 9;
n=4: 16 <= 16 < 32;
...
n=20: 20^4 = 160000 < 1048576 = 2^20 < 3200000; etc.
MATHEMATICA
Table[n^Floor[Log[n, 2^n]], {n, 2, 40}] (* Harvey P. Dale, May 31 2014 *)
PROG
(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
CROSSREFS
Sequence in context: A176737 A370566 A046162 * A113203 A034486 A130515
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 11 2001
STATUS
approved