A308224 Sum of the largest sides 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, 5, 0, 0, 7, 7, 0, 15, 0, 17, 9, 9, 11, 53, 11, 21, 37, 60, 26, 103, 13, 68, 28, 74, 49, 193, 34, 115, 106, 210, 74, 291, 76, 227, 97, 214, 107, 464, 132, 345, 205, 414, 117, 592, 198, 488, 223, 454, 214, 1037, 274, 591, 491

Offset

1,12

Links

Table of n, a(n) for n=1..63.

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] * (n-i-k), where [] is the Iverson Bracket.

Mathematica

Table[Sum[Sum[(n - i - 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. A308223.

Sequence in context: A261852 A254293 A263496 * A200630 A198225 A256929

Adjacent sequences: A308221 A308222 A308223 * A308225 A308226 A308227

Keyword

nonn

Author

Wesley Ivan Hurt, May 16 2019

Status

approved