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 A308225 Take the integer-sided triangles with perimeter n and mutually coprime sides a, b and c such that a <= b <= c. a(n) is the sum of all the b's. 0

%I

%S 0,0,1,0,0,0,0,0,0,0,0,4,0,0,5,5,0,13,0,14,7,8,7,42,9,17,29,49,20,87,

%T 11,59,22,57,37,153,24,94,82,171,58,239,62,185,79,184,81,384,106,283,

%U 163,333,91,484,156,400,181,365,166,840,218,479,385,660,280

%N Take the integer-sided triangles with perimeter n and mutually coprime sides a, b and c such that a <= b <= c. a(n) is the sum of all the b's.

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

%t Table[Sum[Sum[i*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}]

%Y Cf. A308224.

%K nonn

%O 1,12

%A _Wesley Ivan Hurt_, May 16 2019

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Last modified January 22 10:13 EST 2022. Contains 350481 sequences. (Running on oeis4.)