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 A033684 1 iff n is a square not divisible by 3. 4

%I

%S 0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0

%N 1 iff n is a square not divisible by 3.

%C Multiplicative with a(p^e) = 1 if 2 divides e and p != 3, 0 otherwise. _Mitch Harris_ Jun 09, 2005.

%C a(n) * A000035(n) = A033683(n).

%C a(n)=1 iff n-1 is in the list A057780. - _Jason Kimberley_, Nov 13 2012

%D J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, p. 105, Eq (40).

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F Essentially the series psi_3(z)=(1/2)(theta_3(z/9)-theta_3(z)).

%F Dirichlet g.f. zeta(2*s)*(1-3^(-2*s)). - R. J. Mathar, Mar 10 2011

%p A033684 := proc(n)

%p if issqr(n) then

%p if n mod 3 = 0 then

%p 0;

%p else

%p 1;

%p end if;

%p else

%p 0;

%p end if;

%p end proc:

%p seq(A033684(n),n=0..80) ; # R. J. Mathar, Oct 07 2011

%Y Cf. A057780.

%K nonn,easy,mult

%O 0,1

%A _N. J. A. Sloane_.

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