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%I #6 Jun 18 2020 13:58:40
%S 0,0,0,0,1,1,2,1,2,1,2,1,2,2,4,3,4,3,4,3,4,3,4,3,4,3,5,4,6,6,8,8,10,9,
%T 11,10,12,11,14,12,14,12,14,12,14,13,16,15,18,17,20,18,20,19,21,20,22,
%U 20,22,20,22,20,23,21,24,22,25,23,26,24,26,24,26
%N Number of integer-sided triangles with perimeter n and side lengths a, b and c such that a <= b <= c, and b 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(i).
%t Table[Sum[Sum[ (PrimePi[i] - PrimePi[i - 1]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
%Y Cf. A010051, A308451.
%K nonn
%O 1,7
%A _Wesley Ivan Hurt_, May 27 2019
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