A308074 Number of integer-sided triangles with perimeter n whose side lengths are mutually coprime.

0, 0, 1, 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

Offset

1,18

Links

Table of n, a(n) for n=1..77.

Formula

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/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.

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, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

Crossrefs

Sequence in context: A236627 A116664 A295672 * A024161 A035156 A063883

Adjacent sequences: A308071 A308072 A308073 * A308075 A308076 A308077

Keyword

nonn

Author

Wesley Ivan Hurt, May 11 2019

Status

approved