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%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]
%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. Adams-Watters, Sep 11 2005.
%F a(n) = f(n,0) with f(x,y) = if x>0 then f(x-3*y*(y+1),y+1) else 0^(-x). [From _Reinhard Zumkeller_, Sep 27 2008]
%t Table[ Boole[ IntegerQ[n^(1/3)]], {n, 0, 80}] (* _Jean-François Alcover_, Jun 10 2013 *)
%o (Haskell)
%o a010057 n = a010057_list !! n
%o a010057_list = concatMap (\x -> 1 : replicate (a003215 x - 1) 0) [0..]
%o -- _Reinhard Zumkeller_, Oct 22 2011
%Y Cf. A000578.
%Y A003215. [From _Reinhard Zumkeller_, Sep 27 2008]
%K nonn,mult,changed
%O 0,1
%A _N. J. A. Sloane_.
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