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%I #11 Sep 17 2020 16:21:59
%S 0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,1,0,1,2,1,2,1,1,1,1,2,2,1,2,3,4,
%T 2,1,1,2,2,1,0,1,1,2,4,4,2,2,2,3,4,4,5,5,4,7,6,4,2,3,5,4,2,2,3,3,3,5,
%U 8,6,6,7,7,8,7,7,10,9,9,10,12,14,10,7,9
%N Number of integer-sided triangles with perimeter n whose side lengths are semiprime.
%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))) * c(i) * c(k) * c(n-i-k), where c is the semiprime characteristic (A064911).
%t Table[Sum[Sum[KroneckerDelta[PrimeOmega[i], 2] KroneckerDelta[PrimeOmega[k], 2] KroneckerDelta[PrimeOmega[n - i - k], 2]*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
%Y Cf. A064911.
%K nonn
%O 1,22
%A _Wesley Ivan Hurt_, May 10 2019
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