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 A024161 Number of integer-sided triangles with sides a,b,c, a < b < c, a+b+c = n such that a,b,c are pairwise relatively prime. 0

%I

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

%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 22,17,29,12,42,11,32,15,37,11,49,9,32,22,41,15,58,12,48,19,41,18,73,19,46,30,58,22,86,20

%N Number of integer-sided triangles with sides a,b,c, a < b < c, a+b+c = n such that a,b,c are pairwise relatively prime.

%F a(n) = Sum_{k=1..floor((n-1)/3)} Sum_{i=k+1..floor((n-k-1)/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. - _Wesley Ivan Hurt_, May 11 2019

%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 + 1, Floor[(n - k - 1)/2]}], {k, Floor[(n - 1)/3]}], {n, 100}] (* _Wesley Ivan Hurt_, May 11 2019 *)

%K nonn

%O 1,18

%A _Clark Kimberling_

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Last modified May 17 10:16 EDT 2022. Contains 353745 sequences. (Running on oeis4.)