cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A120692 Primitive elements of A065607.

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

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Author

Keywords

Examples

			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.
		

Crossrefs

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

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Author

Ralf Steiner, Feb 04 2018

Keywords

Comments

Conjectures:
12|r, 3|b or 3|c or 3|d, 4|b or 4|c or 4|d.
No term is powerful (A001694) or square (A000290).

Examples

			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,
  ...
		

Crossrefs

Programs

  • Mathematica
    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

Formula

a(n) > 1.

Extensions

a(28)-a(51) from Giovanni Resta, Feb 06 2018
Showing 1-2 of 2 results.