A062278 a(n) = floor(3^n / n^3).

3, 1, 1, 1, 1, 3, 6, 12, 27, 59, 133, 307, 725, 1743, 4251, 10509, 26285, 66430, 169450, 435848, 1129505, 2947131, 7737583, 20430377, 54226471, 144621405, 387420489, 1042127936, 2813988985, 7625597484, 20733556989, 56549688380

Offset: 1

Author

Henry Bottomley, Jul 02 2001

Keywords

• nonn

Comments

3 is the only integer value of k for which floor(n^k / k^n) is always positive. For positive real x and k, the only value of k for which x^k is always greater than or equal to k^x is e = 2.71828...

Examples

			a(2) = floor(3^2 / 2^3) = floor(9/8) = 1.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000244, A000578, A024026, A060505.

Programs

GAP

List([1..35],n->Int(3^n/n^3)); # Muniru A Asiru, Jul 01 2018

Maple

seq(floor(3^n/n^3),n=1..35); # Muniru A Asiru, Jul 01 2018

Mathematica

Table[Floor[3^n/n^3],{n,40}] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)

PARI

{ default(realprecision, 50); for (n=1, 200, write("b062278.txt", n, " ", floor(3^n / n^3)) ) } \\ Harry J. Smith, Aug 03 2009