A308225 Take the integer-sided triangles with perimeter n and mutually coprime sides a, b and c such that a <= b <= c. a(n) is the sum of all the b's.

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 5, 0, 13, 0, 14, 7, 8, 7, 42, 9, 17, 29, 49, 20, 87, 11, 59, 22, 57, 37, 153, 24, 94, 82, 171, 58, 239, 62, 185, 79, 184, 81, 384, 106, 283, 163, 333, 91, 484, 156, 400, 181, 365, 166, 840, 218, 479, 385, 660, 280

Offset

1,12

Links

Table of n, a(n) for n=1..65.

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

Mathematica

Table[Sum[Sum[i*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. A308224.

Sequence in context: A005397 A259124 A273515 * A021718 A193108 A212044

Adjacent sequences: A308222 A308223 A308224 * A308226 A308227 A308228

Keyword

nonn

Author

Wesley Ivan Hurt, May 16 2019

Status

approved