A316842 -id:A316842 - cp's OEIS frontend

A378820 a(n) is the number of distinct nondegenerate triangles whose sides are divisors of n.

1, 3, 3, 6, 3, 11, 3, 10, 6, 10, 3, 26, 3, 10, 11, 15, 3, 23, 3, 23, 10, 10, 3, 46, 6, 10, 10, 22, 3, 45, 3, 21, 10, 10, 11, 57, 3, 10, 10, 43, 3, 41, 3, 21, 24, 10, 3, 70, 6, 21, 10, 21, 3, 39, 10, 42, 10, 10, 3, 114, 3, 10, 23, 28, 10, 39, 3, 21, 10, 42, 3, 108

Offset: 1

Felix Huber, Dec 27 2024

nonn

A divisor can be used for several sides.

A nondegenerate triangle is a triangle whose sides (u, v, w) are such that u + v > w, v + w > u and u + w > v.

			a(4) = 6 because there are the 6 distinct nondegenerate triangles (1, 1, 1), (1, 2, 2), (1, 4, 4), (2, 2, 2), (2, 4, 4), (4, 4, 4) whose sides are divisors of 4. The triples (1, 1, 2), (1, 1, 4), (1, 2, 4), (2, 2, 4) are not sides of (nondegenerate) triangles.

Felix Huber, Table of n, a(n) for n = 1..10000
Wikipedia, Triangle Inequality

Cf. A000005, A316841, A316842, A378819.

A378820:=proc(n)
   local a,i,j,k,L;
   L:=NumberTheory:-Divisors(n);
   a:=0;
   for i to nops(L) do
      for j from i to nops(L) do
         for k from j to nops(L) while L[k]A378820(n),n=1..72);

a(p) = 3 for prime p.

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

A378820 a(n) is the number of distinct nondegenerate triangles whose sides are divisors of n.

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