A308256 - OEIS

%I #8 Jun 18 2020 13:51:59

%S 0,0,1,0,0,0,0,0,4,0,0,4,6,6,0,6,8,14,18,16,28,37,19,37,43,53,31,56,

%T 50,88,86,95,118,148,91,134,130,178,113,165,143,231,212,263,299,361,

%U 224,323,304,409,431,471,475,612,646,684,764,840,644,767,802,909

%N Sum of the largest side lengths of all integer-sided triangles with perimeter n and nonprime sides.

%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))) * A005171(i) * A005171(k) * A005171(n-i-k) * (n-i-k).

%t Table[Sum[Sum[(n - i - k)*(1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[k] + PrimePi[k - 1]) (1 - PrimePi[n - i - k] + PrimePi[n - i - k - 1]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

%Y Cf. A005171, A308253.

%K nonn

%O 1,9

%A _Wesley Ivan Hurt_, May 17 2019