A062838 Cubes of squarefree numbers.

1, 8, 27, 125, 216, 343, 1000, 1331, 2197, 2744, 3375, 4913, 6859, 9261, 10648, 12167, 17576, 24389, 27000, 29791, 35937, 39304, 42875, 50653, 54872, 59319, 68921, 74088, 79507, 97336, 103823, 132651, 148877, 166375, 185193, 195112, 205379, 226981, 238328

Offset: 1

Author

Jason Earls, Jul 21 2001

Keywords

• nonn
• easy

Comments

Cubefull numbers (A036966) all of whose nonunitary divisors are not cubefull (A362147). - Amiram Eldar, May 13 2023

Links

• Vincenzo Librandi and T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Other powers of squarefree numbers: A005117(1), A062503(2), A113849(4), A072774(all).

Cf. A000400, A036966, A225546, A362147.

A329332 column 3 in ascending order.

Programs

Mathematica

Select[Range[70], SquareFreeQ]^3 (* Harvey P. Dale, Jul 20 2011 *)

PARI

for(n=1,35, if(issquarefree(n),print(n*n^2)))

PARI

a(n) = my(m, c); if(n<=1, n==1, c=1; m=1; while(cAltug Alkan, Dec 03 2015

Python

from math import isqrt
from sympy import mobius
def A062838(n):
    def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m**3 # Chai Wah Wu, Sep 11 2024

Formula

A055229(a(n)) = A005117(n) and A055229(m) < A005117(n) for m < a(n). - Reinhard Zumkeller, Apr 09 2010

a(n) = A005117(n)^3. - R. J. Mathar, Dec 03 2015

{a(n)} = {A225546(A000400(n)) : n >= 0}, where {a(n)} denotes the set of integers in the sequence. - Peter Munn, Oct 31 2019

Sum_{n>=1} 1/a(n) = zeta(3)/zeta(6) = 945*zeta(3)/Pi^6 (A157289). - Amiram Eldar, May 22 2020

Extensions

More terms from Dean Hickerson, Jul 24 2001

More terms from Vladimir Joseph Stephan Orlovsky, Aug 15 2008