A308513 - OEIS

%I #7 Jun 16 2020 14:36:50

%S 0,0,0,0,0,2,3,3,7,8,14,10,17,12,25,20,36,31,50,35,63,47,79,62,98,80,

%T 120,87,130,94,140,101,161,120,185,142,212,167,255,209,304,257,359,

%U 289,397,324,438,362,482,403,546,439,589,478,635,520,703,585,777

%N Sum of the largest side lengths of all integer-sided triangles with perimeter n whose smallest side length is prime.

%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))) * A010051(k) * (n-i-k).

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

%Y Cf. A010051, A308450.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, Jun 02 2019