|
|
A371587
|
|
a(n) is the number of integers m from 1 to n inclusive such that m^m is a cube.
|
|
0
|
|
|
1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 28
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Dick Hess gave a puzzle at a "Gathering for Gardner" meeting asking for a(40).
a(n) is the number of integers not exceeding n that are divisible by 3 plus the number of cubes in the same range that are not divisible by 3.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = floor(n/3) + floor(n^(1/3)) - floor(n^(1/3)/3).
|
|
EXAMPLE
|
Suppose n = 40. There are 13 numbers in the range that are divisible by 3 and should be counted. In addition, there are two cubes 1 and 8 that are not divisible by 3. Thus, a(40) = 15.
|
|
MATHEMATICA
|
Table[Floor[n/3] + Floor[n^(1/3)] - Floor[n^(1/3)/3], {n, 100}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|