A024161 Number of integer-sided triangles with sides a,b,c, a < b < c, a+b+c = n such that a,b,c are pairwise relatively prime.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 5, 1, 2, 3, 5, 2, 8, 1, 5, 2, 5, 3, 12, 2, 7, 6, 12, 4, 16, 4, 12, 5, 11, 5, 22, 6, 16, 9, 18, 5, 25, 8, 20, 9, 18, 8, 39, 10, 22, 17, 29, 12, 42, 11, 32, 15, 37, 11, 49, 9, 32, 22, 41, 15, 58, 12, 48, 19, 41, 18, 73, 19, 46, 30, 58, 22, 86, 20

Offset

1,18

Links

Table of n, a(n) for n=1..91.

Formula

a(n) = Sum_{k=1..floor((n-1)/3)} Sum_{i=k+1..floor((n-k-1)/2)} sign(floor((i+k)/(n-i-k+1))) * [gcd(i,k) * gcd(i,n-i-k) * gcd(k,n-i-k) = 1], where [] is the Iverson bracket. - Wesley Ivan Hurt, May 11 2019

Mathematica

Table[Sum[Sum[Floor[1/(GCD[i, k]*GCD[i, n - i - k]*GCD[k, n - i - k])]*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k + 1, Floor[(n - k - 1)/2]}], {k, Floor[(n - 1)/3]}], {n, 100}] (* Wesley Ivan Hurt, May 11 2019 *)

Crossrefs

Sequence in context: A116664 A295672 A308074 * A035156 A063883 A079691

Adjacent sequences: A024158 A024159 A024160 * A024162 A024163 A024164

Keyword

nonn

Author

Clark Kimberling

Status

approved