A371587 a(n) is the number of integers m from 1 to n inclusive such that m^m is a cube.

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

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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}]
Accumulate[Table[If[IntegerQ[CubeRoot[n^n]], 1, 0], {n, 100}]] (* Harvey P. Dale, Aug 12 2025 *)

Prog

(Python)
from sympy import integer_nthroot
def A371587(n): return n//3+integer_nthroot(n, 3)[0]-integer_nthroot(n//27, 3)[0] # Chai Wah Wu, Sep 18 2024

Crossrefs

Cf. A000578, A329547.

Sequence in context: A323701 A226591 A194223 * A194251 A029114 A224710

Adjacent sequences: A371584 A371585 A371586 * A371588 A371589 A371590

Keyword

nonn

Author

Tanya Khovanova, Mar 28 2024

Status

approved