

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
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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



