A057098 - OEIS

%I #5 Nov 21 2019 08:15:41

%S 3,6,5,9,8,12,7,10,15,20,18,9,12,16,21,15,24,14,11,27,20,24,30,16,28,

%T 33,13,40,25,36,21,18,33,24,32,39,42,30,15,48,20,45,36,48,40,35,28,39,

%U 51,22,60,54,17,27,40,57,36,48,65,60,24,32,35,56,63,45,60,19,66,44,56

%N Shortest side of a Pythagorean triangle (ordered by the product of the sides).

%F a(n) =A057096(n)/(A057099(n)*A057100(n)) =sqrt(A057100(n)^2-A057099(n)^2)

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

%t maxShortLeg = 66; terms = 71;

%t r[a_] := {a, b, c} /. {ToRules[Reduce[a <= b < c && a^2+b^2 == c^2, {b, c}, Integers]]};

%t abc = r /@ Complement[Range[maxShortLeg], {1, 2, 4}] // Flatten[#, 1]&;

%t SortBy[abc, Times @@ # &][[;; terms, 1]] (* _Jean-François Alcover_, Nov 21 2019 *)

%Y Cf. A009004, A009005, A046083, A057096.

%K nonn

%O 1,1

%A _Henry Bottomley_, Aug 01 2000