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

Author

Felix Huber, Dec 27 2024

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000005, A316841, A316842, A378819.

Programs

Maple

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);

Formula

a(p) = 3 for prime p.