A308202 Number of integer-sided triangles with perimeter n such that the length of the smallest side is coprime to n.

0, 0, 1, 0, 1, 0, 2, 0, 2, 1, 4, 0, 5, 1, 4, 2, 8, 2, 10, 1, 7, 4, 14, 4, 13, 6, 13, 4, 21, 3, 24, 9, 17, 11, 20, 7, 33, 13, 24, 13, 40, 9, 44, 13, 24, 20, 52, 15, 48, 19, 40, 20, 65, 18, 50, 27, 49, 33, 80, 21, 85, 37, 50, 40, 70, 24, 102, 37, 71, 32, 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(k,n) = 1], where [] is the Iverson bracket.

Mathematica

Table[Sum[Sum[Floor[1/GCD[k, n]] 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: A295689 A305804 A053470 * A329152 A368581 A337563

Adjacent sequences: A308199 A308200 A308201 * A308203 A308204 A308205

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved