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A308074 Number of integer-sided triangles with perimeter n whose side lengths are mutually coprime. 4

%I

%S 0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,2,0,2,1,1,1,5,1,2,3,5,2,8,1,5,2,5,

%T 3,12,2,7,6,12,4,16,4,12,5,11,5,22,6,16,9,18,5,25,8,20,9,18,8,39,10,

%U 22,17,29,12,42,11,32,15,37,11,49,9,32,22,41,15

%N Number of integer-sided triangles with perimeter n whose side lengths are mutually coprime.

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

%t Table[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}]

%K nonn

%O 1,18

%A _Wesley Ivan Hurt_, May 11 2019

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Last modified January 16 19:48 EST 2022. Contains 350376 sequences. (Running on oeis4.)