A060509 Largest power of n not exceeding 2^n.

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

Harry J. Smith, Table of n, a(n) for n = 2..200

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: A038233 A176737 A046162 * A113203 A034486 A130515

Adjacent sequences: A060506 A060507 A060508 * A060510 A060511 A060512

Keyword

nonn

Author

Labos Elemer, Apr 11 2001

Status

approved