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A308202 Number of integer-sided triangles with perimeter n such that the length of the smallest side is coprime to n. 1

%I

%S 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,

%T 9,17,11,20,7,33,13,24,13,40,9,44,13,24,20,52,15,48,19,40,20,65,18,50,

%U 27,49,33,80,21,85,37,50,40,70,24,102,37,71,32,114

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>

%F 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.

%t 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}]

%Y Cf. A308074.

%K nonn

%O 1,7

%A _Wesley Ivan Hurt_, May 15 2019

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Last modified January 28 17:08 EST 2023. Contains 359895 sequences. (Running on oeis4.)