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.
A120693
Elements of A065607 from primitive triples.
Original entry on oeis.org
20, 156, 255, 600, 609, 1295, 1640, 2385, 3640, 3660, 4015, 4095, 6545, 6984, 7120, 7140, 9919, 9999, 12656, 14385, 14625, 20280, 20724, 20735, 20860, 20880, 28305, 28545, 31980, 32424, 32560, 32580, 37791, 38335, 38415, 48464, 48620, 50369
Offset: 1
156 is part of the triple 60,65,156. 600 is part of the primitive triple 168,175,600; it is included here but excluded from A120692.
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
Original entry on oeis.org
0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880
Offset: 0
-
Table[40 n, {n, 0, 50}] (* or *)
LinearRecurrence[{2, -1}, {0, 40}, 50] (* or *)
CoefficientList[Series[40*x/(1 - x)^2, {x, 0, 50}], x] (* Stefano Spezia, Sep 07 2018 *)
-
a(n) = 40*n
-
a(n) = if(n==0, 0, if(n==1, 40, 2*a(n-1)-a(n-2)))
-
concat(0, Vec(40*x/(1-x)^2 + O(x^60)))
A065709
Reduced sequence related to reciprocal Pythagorean triples: 1/a(n)^2 + 1/k^2 = 1/j^2 has an integer solution (k,j) with k
Original entry on oeis.org
156, 255, 312, 468, 510, 609, 624, 765, 936, 1092, 1218, 1248, 1275, 1295, 1404, 1530, 1716, 1785, 1827, 1872, 2028, 2184, 2295, 2385, 2436, 2496, 2550, 2590, 2652, 2805, 2808, 2964, 3045, 3276, 3315, 3432, 3570, 3588, 3654, 3744, 3825, 3885, 4015, 4056, 4095
Offset: 1
a(10)=1218: 1/a(10)^2 + 1/1160^2 = 1/840^2
Showing 1-5 of 5 results.
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