OFFSET
1,1
COMMENTS
Numbers n such that A297968(n) > 0.
All terms are even.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
MAPLE
filter:= proc(n) local d, x, s, ys;
d:= numtheory:-divisors(n);
for x in d do
if issqr(x^4+4*n*x) then
s:= sqrt(x^4+4*n*x);
ys:= select(t -> type(t, integer) and igcd(t, x)=1, [-(s+x^2)/(2*x), (x^2-s)/(2*x)]);
if ys <> [] then return true fi;
fi
od;
false
end proc:
select(filter, [seq(i, i=1..10000, 2)]);
MATHEMATICA
f[n_] := Module[{d, count, x, s, ys}, d = Divisors[n]; count = 0; Do[If[ IntegerQ[Sqrt[x^4 + 4 n x]], s = Sqrt[x^4 + 4 n x]; ys = Select[{-(s + x^2)/(2x), (x^2 - s)/(2x)}, IntegerQ[#] && GCD[#, x] == 1&]; count = count + Length[ys]], {x, Union[d, -d]}]; count];
Position[Array[f, 2000], _?Positive] // Flatten (* Jean-François Alcover, Apr 29 2019, after Robert Israel in A297968 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Jan 10 2018
STATUS
approved