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

1,2

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

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

Mathematica

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

Prog

(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(c<n, m++; if(issquarefree(m), c++)); m^3); \\ Altug 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

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.

Sequence in context: A030160 A030162 A153147 * A240859 A277047 A046452

Adjacent sequences: A062835 A062836 A062837 * A062839 A062840 A062841

Keyword

nonn,easy

Author

Jason Earls, Jul 21 2001

Extensions

More terms from Dean Hickerson, Jul 24 2001

More terms from Vladimir Joseph Stephan Orlovsky, Aug 15 2008

Status

approved