|
|
A033684
|
|
1 iff n is a square not divisible by 3.
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
|
|
REFERENCES
|
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, p. 105, Eq. (40).
|
|
LINKS
|
|
|
FORMULA
|
Essentially the series psi_3(z)=(1/2)(theta_3(z/9)-theta_3(z)).
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
Sum_{k=1..n} a(k) ~ 2*sqrt(n)/3. - Amiram Eldar, Jan 14 2024
|
|
MAPLE
|
if issqr(n) then
if n mod 3 = 0 then
0;
else
1;
end if;
else
0;
end if;
end proc:
|
|
MATHEMATICA
|
Table[If[IntegerQ[Sqrt[n]]&&Mod[n, 3]!=0, 1, 0], {n, 0, 130}] (* Harvey P. Dale, Oct 19 2018 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,mult
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|