A232461 -id:A232461 - cp's OEIS frontend

A329536 Integer areas of integer-sided triangles where the lengths of two of the sides are cubes.

480, 4200, 5148, 7500, 30720, 65520, 268800, 329472, 349920, 480000, 960960, 1684980, 1713660, 1884960, 1966080, 2413320, 2419560, 3061800, 3752892, 4193280, 5467500, 7500000, 8168160, 10022520, 11166960, 17203200, 17915040, 18462300, 21086208, 22394880, 28964040

Offset: 1

Michel Lagneau, Nov 16 2019

nonn

Subset of A188158.
The area of the triangle (a,b,c) are given by Heron's formula, A = sqrt(s(s-a)(s-b)(s-c)), where the side lengths are a, b, c and semiperimeter s = (a+b+c)/2.
The areas of the nonprimitive triangles of sides (a*k^3, b*k^3, c*k^3), k = 1,2,... are in the sequence with the value A*k^6.
There may be multiple triangles with the same area (see the table of examples below).

			The following table gives the initial values of (A, a, b, c):
+--------+------+-------+-------+
|     A  |    a |     b |    c  |
+--------+------+-------+-------+
|    480 |    8 |   123 |   125 |
|   4200 |   70 |   125 |   125 |
|   4200 |  125 |   125 |   240 |
|   5148 |   88 |   125 |   125 |
|   5148 |  125 |   125 |   234 |
|   7500 |  125 |   125 |   150 |
|   7500 |  125 |   125 |   200 |
|  30720 |   64 |   984 |  1000 |
|  65520 |  125 |  2088 |  2197 |
| 268800 |  560 |  1000 |  1000 |
| 268800 | 1000 |  1000 |  1920 |
| 329472 |  704 |  1000 |  1000 |
| 329472 | 1000 |  1000 |  1872 |
| 349920 |  216 |  3321 |  3375 |
.................................

Cf. A188158, A232461.

nn=600;lst={};Do[s=(a^3+b^3+c)/2;If[IntegerQ[s],area2=s (s-a^3)(s-b^3) (s-c);If[0

cp's OEIS Frontend

A329536 Integer areas of integer-sided triangles where the lengths of two of the sides are cubes.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica