A152411 Nonnegative integers representable as m^2 - n^4 for positive integers m,n.

0, 3, 8, 9, 15, 19, 20, 24, 33, 35, 40, 48, 51, 63, 65, 68, 73, 80, 84, 88, 99, 104, 105, 115, 120, 128, 129, 143, 144, 148, 153, 159, 163, 168, 175, 180, 185, 195, 200, 201, 208, 209, 216, 224, 225, 228, 240, 243, 255, 260, 273, 275, 280, 288, 289, 303, 304, 308, 319, 320

Offset: 1

Author

N. J. A. Sloane, Oct 24 2009, based on email from Joerg Arndt, Oct 10 2009

Keywords

• nonn

Comments

Nonnegative integers representable as the product u*v with (u-v)/2 being a positive square.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A087286, A165289, A152412.

Programs

Maple

filter:= proc(x) local d,u;
  d:= select(t -> t^2 > x, numtheory:-divisors(x));
  for u in d do if issqr((u-x/u)/2) then return true fi od;
  false
end proc:
filter(0):= true:
select(filter, [$0..1000]); # Robert Israel, Nov 06 2017

Mathematica

filterQ[x_] := Catch[With[{d = Select[Divisors[x], #^2 > x&]}, Do[If[IntegerQ[Sqrt[(u-x/u)/2]], Throw[True]], {u, d}]; Throw[False]]];
filterQ[0] = True;
Select[Range[0, 1000], filterQ] (* Jean-François Alcover, Jul 24 2020, after Robert Israel *)

PARI

for(k=1,1000, fordiv(k,d, if(d*d>=k,break); if( issquare((k\d - d)/2), print1(k,", "); break) ) )

Extensions

Edited and extended by Max Alekseyev, Feb 06 2010