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

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, 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, 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, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0,1

Comments

a(n)=1 iff n-1 is in the list A057780. - Jason Kimberley, Nov 13 2012

References

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

Links

Antti Karttunen, Table of n, a(n) for n = 0..65536

Index entries for characteristic functions.

Formula

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

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

Multiplicative with a(p^e) = 1 if 2 divides e and p != 3, 0 otherwise. - Mitch Harris, Jun 09 2005

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

a(n) = A010052(n)*A011655(n). - Antti Karttunen, Sep 13 2017

Sum_{k=1..n} a(k) ~ 2*sqrt(n)/3. - Amiram Eldar, Jan 14 2024

Maple

A033684 := proc(n)
        if issqr(n) then
                if n mod 3 = 0 then
                        0;
                else
                        1;
                end if;
        else
                0;
        end if;
end proc:
seq(A033684(n), n=0..80) ; # R. J. Mathar, Oct 07 2011

Mathematica

Table[If[IntegerQ[Sqrt[n]]&&Mod[n, 3]!=0, 1, 0], {n, 0, 130}] (* Harvey P. Dale, Oct 19 2018 *)

Prog

(PARI) A033684(n) = (issquare(n)&&(n%3)); \\ Antti Karttunen, Sep 13 2017

Crossrefs

Cf. A010052, A011655, A033683, A057780.

Sequence in context: A356922 A106701 A258021 * A080885 A258998 A363713

Adjacent sequences: A033681 A033682 A033683 * A033685 A033686 A033687

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Extensions

Data-section extended up to a(121) by Antti Karttunen, Sep 13 2017

Status

approved