A057099 Middle side of a Pythagorean triangle (ordered by the product of the sides).

4, 8, 12, 12, 15, 16, 24, 24, 20, 21, 24, 40, 35, 30, 28, 36, 32, 48, 60, 36, 48, 45, 40, 63, 45, 44, 84, 42, 60, 48, 72, 80, 56, 70, 60, 52, 56, 72, 112, 55, 99, 60, 77, 64, 75, 84, 96, 80, 68, 120, 63, 72, 144, 120, 96, 76, 105, 90, 72, 80, 143, 126, 120, 90, 84, 108, 91

Offset: 1

Author

Henry Bottomley, Aug 01 2000

Keywords

• nonn

Examples

			a(1)=4 since 3*4*5=60 is smallest possible positive product
		

Crossrefs

Cf. A009012, A009023, A046084, A057096.

Programs

Mathematica

maxShortLeg = 66; terms = 67;
r[a_] := {a, b, c} /. {ToRules[Reduce[a <= b < c && a^2+b^2 == c^2, {b, c}, Integers]]};
abc = r /@ Complement[Range[maxShortLeg], {1, 2, 4}] // Flatten[#, 1]&;
SortBy[abc, Times @@ # &][[;; terms, 2]] (* Jean-François Alcover, Nov 21 2019 *)

Formula

a(n) =A057096(n)/(A057098(n)*A057100(n)) =sqrt(A057100(n)^2-A057098(n)^2)