A308223 Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose side lengths are mutually coprime.

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 4, 0, 8, 0, 9, 5, 5, 5, 25, 5, 14, 15, 31, 12, 50, 7, 33, 16, 39, 19, 86, 16, 57, 46, 99, 32, 142, 34, 116, 49, 108, 47, 208, 56, 172, 91, 189, 57, 274, 86, 232, 109, 225, 92, 463, 118, 294, 195, 378, 150, 562

Offset

1,12

Links

Table of n, a(n) for n=1..66.

Wikipedia, Integer Triangle

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] * k, where [] is the Iverson Bracket.

Mathematica

Table[Sum[Sum[k*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

Cf. A308074.

Sequence in context: A279168 A111787 A200524 * A222328 A222402 A222522

Adjacent sequences: A308220 A308221 A308222 * A308224 A308225 A308226

Keyword

nonn

Author

Wesley Ivan Hurt, May 16 2019

Status

approved