|
|
A062278
|
|
a(n) = floor(3^n / n^3).
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
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...
|
|
LINKS
|
|
|
EXAMPLE
|
a(2) = floor(3^2 / 2^3) = floor(9/8) = 1.
|
|
MAPLE
|
|
|
MATHEMATICA
|
|
|
PROG
|
(PARI) { default(realprecision, 50); for (n=1, 200, write("b062278.txt", n, " ", floor(3^n / n^3)) ) } \\ Harry J. Smith, Aug 03 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|