A317181 -id:A317181 - cp's OEIS frontend

A316842 Three-column table read by rows giving primitive integer sides of proper triangles (i,j,k) with i >= j >= k >= 1, j+k > i, gcd(i,j,k) = 1.

1, 1, 1, 2, 2, 1, 3, 2, 2, 3, 3, 1, 3, 3, 2, 4, 3, 2, 4, 3, 3, 4, 4, 1, 4, 4, 3, 5, 3, 3, 5, 4, 2, 5, 4, 3, 5, 4, 4, 5, 5, 1, 5, 5, 2, 5, 5, 3, 5, 5, 4, 6, 4, 3, 6, 5, 2, 6, 5, 3, 6, 5, 4, 6, 5, 5, 6, 6, 1, 6, 6, 5, 7, 4, 4, 7, 5, 3, 7, 5, 4, 7, 5, 5, 7, 6, 2, 7, 6, 3, 7, 6, 4, 7, 6, 5, 7, 6, 6, 7, 7, 1, 7, 7, 2, 7, 7, 3, 7, 7, 4, 7, 7, 5, 7, 7, 6, 8, 5, 4

Offset: 1

N. J. A. Sloane, Jul 23 2018, following a suggestion from Donald S. McDonald

			Table begins:
[1,1,1],
[2,2,1],
[3,2,2],
[3,3,1],
[3,3,2],
[4,3,2],
[4,3,3],
[4,4,1],
[4,4,3],
[5,3,3],
[5,4,2],
...

Lars Blomberg, Table of n, a(n) for n = 1..9000

There are A123323(k) rows that begin with k.
The three columns are A316846, A316847, A316848.
A316850 is a compressed version.
See A316841 for all triples (including imprimitive triples).
See A316852 and A317181 & A317183 for perimeter and area.
Other related sequences: A051493, A070080, A070081, A070082, A070110.

A317183 Numbers k such that k = 16*area(T)^2 for a primitive integer triangle, T.

Original entry on oeis.org

3, 15, 35, 63, 99, 128, 135, 143, 195, 231, 255, 275, 320, 323, 351, 384, 399, 455, 483, 495, 575, 576, 663, 675, 735, 768, 783, 819, 855, 896, 899, 935, 975, 1023, 1071, 1155, 1235, 1280, 1295, 1311, 1344, 1443, 1463, 1536, 1539, 1575, 1599, 1683, 1728, 1763

Offset: 1

N. J. A. Sloane, Jul 25 2018

nonn

A316842 lists the primitive integer triangles.

Lars Blomberg, Table of n, a(n) for n = 1..10000

Cf. A316842.
Sorted and uniqued values of A317181.
Subsequence of A317182.

Terms a(13) and beyond from Lars Blomberg, Jul 27 2018

Name edited by Peter Munn, Jul 30 2025

cp's OEIS Frontend

A316842 Three-column table read by rows giving primitive integer sides of proper triangles (i,j,k) with i >= j >= k >= 1, j+k > i, gcd(i,j,k) = 1.

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