%I
%S 1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0
%N 1 if n is a cube else 0.
%C Multiplicative with a(p^e) = 1 if 3 divides e, 0 otherwise.  _Mitch Harris_ Jun 09, 2005.
%C a(A000578(n)) = 1; a(A007412(n)) = 0.  _Reinhard Zumkeller_, Oct 22 2011
%C a(n) = A000007(sum(A010872(A124010(n,k))): k = 1..A001221(n)) for n > 0.  _Reinhard Zumkeller_, Jun 21 2013
%C If n has 4 divisors, a(n) = bigomega(n)  2.  _Wesley Ivan Hurt_, Jun 06 2014
%D E. Landau, Elementary Number Theory, translation by Jacob E. Goodman of Elementare Zahlentheorie (Vol. I_1 (1927) of Vorlesungen ueber Zahlentheorie), by Edmund Landau, with added exercises by Paul T. Bateman and E. E. Kohlbecker, Chelsea Publishing Co., New York, 1958, pp. 3132.
%H Reinhard Zumkeller, <a href="/A010057/b010057.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F Dirichlet generating function: zeta(3s).  _Franklin T. AdamsWatters_, Sep 11 2005.
%F a(n) = f(n,0) with f(x,y) = if x>0 then f(x3*y*(y+1),y+1) else 0^(x).  _Reinhard Zumkeller_, Sep 27 2008
%F a(n) = 1 + floor(n^(1/3))  ceiling(n^(1/3)).  _Wesley Ivan Hurt_, Jun 06 2014
%t Table[ Boole[ IntegerQ[n^(1/3)]], {n, 0, 80}] (* _JeanFrançois Alcover_, Jun 10 2013 *)
%o (Haskell)
%o a010057 0 = 1
%o a010057 n = fromEnum $ all ((== 0) . (`mod` 3)) $ a124010_row n
%o a010057_list = concatMap (\x > 1 : replicate (a003215 x  1) 0) [0..]
%o  _Reinhard Zumkeller_, Jun 21 2013, Oct 22 2011
%Y Cf. A000578.
%Y Cf. A003215.  _Reinhard Zumkeller_, Sep 27 2008
%K nonn,easy,mult
%O 0,1
%A _N. J. A. Sloane_, March 15 1996
