A308165 - OEIS

%I #6 Jun 18 2020 13:42:25

%S 0,0,0,0,0,6,7,8,9,0,11,12,13,0,30,16,34,0,19,0,21,0,23,24,50,0,81,28,

%T 87,0,62,0,66,0,105,36,111,0,195,40,205,0,172,0,135,0,235,48,245,0,

%U 204,0,212,0,110,0,171,0,295,60,183,0,378,64,520,0,335,0

%N Sum of the perimeters of all integer-sided triangles with perimeter n and prime sides.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>

%F a(n) = n * A070088(n).

%F a(n) = n * Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * A010051(i) * A010051(k) * A010051(n-i-k).

%t Table[n*Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[k] - PrimePi[k - 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. A070088.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, May 15 2019