A308209 Number of integer-sided triangles with perimeter n whose largest side length is coprime to n.

0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 4, 2, 5, 1, 4, 3, 8, 2, 10, 5, 7, 3, 14, 5, 13, 5, 13, 9, 21, 7, 24, 12, 17, 9, 20, 10, 33, 12, 24, 15, 40, 13, 44, 22, 24, 18, 52, 18, 48, 22, 40, 30, 65, 21, 50, 31, 49, 30, 80, 19, 85, 35, 50, 45, 70, 32, 102, 51, 71, 42, 114

Offset

1,7

Links

Table of n, a(n) for n=1..71.

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(n-i-k,n) = 1], where [] is the Iverson bracket.

Mathematica

Table[Sum[Sum[Floor[1/GCD[n - i - k, n]] Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

Crossrefs

Cf. A308202.

Sequence in context: A070963 A174064 A139158 * A366403 A212215 A182270

Adjacent sequences: A308206 A308207 A308208 * A308210 A308211 A308212

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved