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%I #12 Nov 10 2021 17:35:46
%S 20,24,40,42,48,60,72,80,84,96,100,110,112,120,126,130,140,144,156,
%T 160,168,180,192,198,200,210,216,220,224,238,240,252,260,264,266,272,
%U 280,286,288,294,300,304,308,312,320,330,336,340,342,360,364,378,380,384,390,396,400,408
%N Numbers k with positive integer solutions a,b,c such that 2*a^2 + b^2 = c^2, k = a + b + c, and a <= b <= c.
%e 20 is in the sequence since 20 = 4 + 7 + 9 and 2*4^2 + 7^2 = 9^2.
%t Select[Range[400], Length @ Reduce[a + b + c == # && 0 < a <= b <= c && 2*a^2 + b^2 == c^2, {a, b, c}, Integers] > 0 &] (* _Amiram Eldar_, Nov 07 2021 *)
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Nov 07 2021