Original entry on oeis.org
20, 156, 255, 609, 1295, 2385, 4015, 4095, 6545, 6984, 9919, 9999, 12656, 14385, 14625, 20724, 20735, 28545, 32424, 37791, 38335, 38415, 48464, 50369, 50609, 64911, 65455, 69804, 82225, 83265, 83505, 96016, 97056, 97636, 102575, 104351
Offset: 1
156 is part of the triple 60,65,156. Although 600 is part of the primitive triple 168,175,600, it is excluded because it is a multiple of 20.
A299170
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.
Original entry on oeis.org
156, 65, 45, 156, 80, 65, 255, 136, 90, 255, 160, 136, 609, 580, 315, 609, 580, 560, 1295, 444, 315, 1295, 560, 444, 1428, 221, 91, 1560, 1547, 170, 1640, 369, 270, 1640, 480, 369, 1833, 884, 799, 1924, 663, 629, 2385, 1484, 945, 2385, 1680, 1484, 2925, 1100, 429
Offset: 1
1/156^2 + 1/65^2 + 1/45^2 = 1/36^2 = 1/(12*3)^2.
As an array, sequence begins:
156, 65, 45
156, 80, 65,
255, 136, 90,
255, 160, 136,
609, 580, 315,
609, 580, 560,
1295, 444, 315,
1295, 560, 444,
1428, 221, 91,
1560, 1547, 170,
1640, 369, 270,
1640, 480, 369,
1833, 884, 799,
1924, 663, 629,
...
-
n = 1500; lst = {}; Do[Do[Do[If[GCD[b, c, d] == 1,
r = Sqrt[1/(1/b^2 + 1/c^2 + 1/d^2)];
If[IntegerQ[r], lst = AppendTo[lst, {b, c, d}]]], {d, c - 1}],
{c, b - 1}], {b, n}]; lst//Flatten
Showing 1-2 of 2 results.
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