cp's OEIS Frontend

A062838 Cubes of squarefree numbers.

%I A062838 #60 Sep 11 2024 23:47:38
%S A062838 1,8,27,125,216,343,1000,1331,2197,2744,3375,4913,6859,9261,10648,
%T A062838 12167,17576,24389,27000,29791,35937,39304,42875,50653,54872,59319,
%U A062838 68921,74088,79507,97336,103823,132651,148877,166375,185193,195112,205379,226981,238328
%N A062838 Cubes of squarefree numbers.
%C A062838 Cubefull numbers (A036966) all of whose nonunitary divisors are not cubefull (A362147). - _Amiram Eldar_, May 13 2023
%H A062838 Vincenzo Librandi and T. D. Noe, <a href="/A062838/b062838.txt">Table of n, a(n) for n = 1..1000</a>
%F A062838 A055229(a(n)) = A005117(n) and A055229(m) < A005117(n) for m < a(n). - _Reinhard Zumkeller_, Apr 09 2010
%F A062838 a(n) = A005117(n)^3. - _R. J. Mathar_, Dec 03 2015
%F A062838 {a(n)} = {A225546(A000400(n)) : n >= 0}, where {a(n)} denotes the set of integers in the sequence. - _Peter Munn_, Oct 31 2019
%F A062838 Sum_{n>=1} 1/a(n) = zeta(3)/zeta(6) = 945*zeta(3)/Pi^6 (A157289). - _Amiram Eldar_, May 22 2020
%t A062838 Select[Range[70], SquareFreeQ]^3 (* _Harvey P. Dale_, Jul 20 2011 *)
%o A062838 (PARI) for(n=1,35, if(issquarefree(n),print(n*n^2)))
%o A062838 (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
%o A062838 (Python)
%o A062838 from math import isqrt
%o A062838 from sympy import mobius
%o A062838 def A062838(n):
%o A062838     def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
%o A062838     m, k = n, f(n)
%o A062838     while m != k: m, k = k, f(k)
%o A062838     return m**3 # _Chai Wah Wu_, Sep 11 2024
%Y A062838 Other powers of squarefree numbers: A005117(1), A062503(2), A113849(4), A072774(all).
%Y A062838 Cf. A000400, A036966, A225546, A362147.
%Y A062838 A329332 column 3 in ascending order.
%K A062838 nonn,easy
%O A062838 1,2
%A A062838 _Jason Earls_, Jul 21 2001
%E A062838 More terms from _Dean Hickerson_, Jul 24 2001
%E A062838 More terms from _Vladimir Joseph Stephan Orlovsky_, Aug 15 2008