A308229 Sum of the perimeters of all triangles with perimeter n whose side lengths are mutually coprime.

0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 15, 16, 0, 36, 0, 40, 21, 22, 23, 120, 25, 52, 81, 140, 58, 240, 31, 160, 66, 170, 105, 432, 74, 266, 234, 480, 164, 672, 172, 528, 225, 506, 235, 1056, 294, 800, 459, 936, 265, 1350, 440, 1120, 513, 1044, 472, 2340

Offset

1,3

Links

Table of n, a(n) for n=1..60.

Wikipedia, Integer Triangle

Formula

a(n) = n * A308074(n).

a(n) = 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[n*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

Cf. A308074.

Sequence in context: A062535 A063667 A171063 * A318673 A151795 A375199

Adjacent sequences: A308226 A308227 A308228 * A308230 A308231 A308232

Keyword

nonn

Author

Wesley Ivan Hurt, May 16 2019

Status

approved