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

1,2

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.

Links

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

Wikipedia, Triangle Inequality

Formula

a(p) = 3 for prime p.

Example

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.

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]<L[i]+L[j] do
            a:=a+1;
         od
      od
   od;
   return a
end proc;
seq(A378820(n), n=1..72);

Crossrefs

Cf. A000005, A316841, A316842, A378819.

Sequence in context: A184389 A163163 A376646 * A323349 A307982 A339335

Adjacent sequences: A378817 A378818 A378819 * A378821 A378822 A378823

Keyword

nonn,new

Author

Felix Huber, Dec 27 2024

Status

approved