A308255 - OEIS

%I #8 Jun 18 2020 13:51:15

%S 0,0,1,0,0,0,0,0,1,0,0,4,1,4,0,4,1,10,5,10,11,20,10,24,19,32,23,35,24,

%T 51,36,53,54,74,46,73,56,91,63,89,64,121,91,136,136,173,109,168,133,

%U 202,189,232,204,290,270,318,328,381,293,375,356,435,365,436

%N Sum of the smallest 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) * k.

%t Table[Sum[Sum[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 1,12

%A _Wesley Ivan Hurt_, May 17 2019