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A298010 Numbers n such that x*y*(x+y) = n has at least one solution in coprime integers. 2
2, 6, 12, 20, 30, 42, 56, 70, 72, 84, 90, 110, 120, 126, 132, 156, 180, 182, 198, 210, 240, 264, 272, 286, 306, 308, 330, 342, 380, 390, 420, 462, 468, 506, 510, 520, 546, 552, 600, 624, 630, 646, 650, 660, 702, 714, 756, 798, 812, 840, 870, 880, 884, 912, 930, 966, 992, 1008, 1020, 1056, 1122 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers n such that A297968(n) > 0.
All terms are even.
LINKS
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
Cf. A297968.
Sequence in context: A254949 A034100 A034110 * A118373 A077252 A102069
KEYWORD
nonn
AUTHOR
Robert Israel, Jan 10 2018
STATUS
approved

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Last modified June 25 12:23 EDT 2024. Contains 373701 sequences. (Running on oeis4.)