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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A334590 Number of nonprimitive Heronian triangles with perimeter A334589(n).

Original entry on oeis.org

1, 1, 2, 2, 1, 2, 2, 4, 2, 3, 1, 2, 4, 2, 7, 2, 4, 3, 5, 3, 1, 2, 7, 3, 1, 2, 5, 4, 9, 2, 9, 8, 6, 2, 6, 2, 3, 5, 13, 2, 7, 3, 2, 9, 2, 12, 9, 1, 9, 8, 3, 1, 7, 13, 8, 13, 3, 1, 4, 7, 10, 20, 1, 3, 16, 2, 2, 1, 2, 4, 8, 13, 3, 1, 3, 7, 3, 19, 3, 15, 15, 13, 6, 1, 6, 21, 22, 6, 2, 15, 12
Offset: 1

Views

Author

Wesley Ivan Hurt, May 06 2020

Keywords

Examples

			a(1) = 1; there is one nonprimitive Heronian triangle with a perimeter of A334589(1) = 24, which is [6,8,10].
a(2) = 1; there is one nonprimitive Heronian triangle with a perimeter of A334589(2) = 32, which is [10,10,12].

Links

Crossrefs

Cf. A051518, A096468, A334589.

A305888 Numbers that are the perimeter of a Heronian triangle, but not of a primitive Heronian triangle.

Original entry on oeis.org

24, 88, 280, 472, 558, 664, 696, 852, 856, 1048, 1432, 1720, 1816, 2008, 2180, 2292, 2680, 2776, 2868, 3144, 3352, 3544, 3576, 3582, 3732, 3736, 3860, 3928, 4192, 4308, 4504, 4696, 4878, 4976, 5080, 5172, 5272, 5464, 5598, 5748, 6520, 6616, 6740, 6744, 7188
Offset: 1

Views

Author

Giovanni Resta, Jun 14 2018

Keywords

Comments

Numbers in A051518 that are not in A096468.

Examples

			The only Heronian triangle with perimeter 24 has sides {6, 8, 10} and thus it is not primitive. Hence 24 is in the sequence.

Links

Crossrefs

Cf. A051518, A096468.

Programs

  • Mathematica
    hpp[p_] := Catch@Block[{t=0, c, q=p/2}, Do[c = p-a-b; If[c >= b && a+c > b && a+b > c && IntegerQ@ Sqrt[q (q-a) (q-b) (q-c)], t++; If[GCD[a, b, c] == 1, Throw@ False]], {a, p/3}, {b, a, p-a-1}]; t > 0]; Select[2 Range[350], hpp]

A334677 Number of integer-sided triangles with nonintegral area and perimeter A009005(n).

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 2, 4, 2, 5, 4, 7, 4, 8, 6, 10, 8, 12, 10, 14, 11, 16, 14, 19, 16, 21, 18, 24, 19, 27, 24, 30, 23, 33, 30, 37, 32, 40, 35, 44, 39, 48, 44, 52, 45, 56, 50, 61, 56, 65, 57, 70, 64, 75, 70, 80, 72, 85, 80, 91, 80, 96, 90, 102, 95, 108, 100, 114, 103, 120, 114
Offset: 1

Views

Author

Wesley Ivan Hurt, May 08 2020

Keywords

Examples

			a(1) = 1; There is one integer-sided triangle with perimeter A009005(1) = 3 whose area is not an integer, [1,1,1] with area sqrt(3)/4.
a(2) = 1; There is one integer-sided triangle with perimeter A009005(2) = 5 whose area is not an integer, [1,2,2] with area sqrt(15)/4.

Links

Crossrefs

Cf. A005044, A009005, A051516, A051518.
Previous Showing 21-23 of 23 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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