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%I #86 Mar 04 2018 15:55:12
%S 156,65,45,156,80,65,255,136,90,255,160,136,609,580,315,609,580,560,
%T 1295,444,315,1295,560,444,1428,221,91,1560,1547,170,1640,369,270,
%U 1640,480,369,1833,884,799,1924,663,629,2385,1484,945,2385,1680,1484,2925,1100,429
%N List of integer triples (b,c,d) where b > c > d are coprime and 1/b^2 + 1/c^2 + 1/d^2 = 1/r^2 and r is an integer, ordered by b then c.
%C Conjectures:
%C 12|r, 3|b or 3|c or 3|d, 4|b or 4|c or 4|d.
%C No term is powerful (A001694) or square (A000290).
%H Giovanni Resta, <a href="/A299170/b299170.txt">Table of n, a(n) for n = 1..570</a>
%F a(n) > 1.
%e 1/156^2 + 1/65^2 + 1/45^2 = 1/36^2 = 1/(12*3)^2.
%e As an array, sequence begins:
%e 156, 65, 45
%e 156, 80, 65,
%e 255, 136, 90,
%e 255, 160, 136,
%e 609, 580, 315,
%e 609, 580, 560,
%e 1295, 444, 315,
%e 1295, 560, 444,
%e 1428, 221, 91,
%e 1560, 1547, 170,
%e 1640, 369, 270,
%e 1640, 480, 369,
%e 1833, 884, 799,
%e 1924, 663, 629,
%e ...
%t n = 1500; lst = {}; Do[Do[Do[If[GCD[b, c, d] == 1,
%t r = Sqrt[1/(1/b^2 + 1/c^2 + 1/d^2)];
%t If[IntegerQ[r], lst = AppendTo[lst, {b, c, d}]]], {d, c - 1}],
%t {c, b - 1}], {b, n}]; lst//Flatten
%Y Cf. A065607, A120692, A120693.
%K nonn,tabf
%O 1,1
%A _Ralf Steiner_, Feb 04 2018
%E a(28)-a(51) from _Giovanni Resta_, Feb 06 2018
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