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%I
%S 0,0,0,0,0,1,1,1,2,2,3,2,3,2,4,3,5,4,6,4,7,5,8,6,9,7,10,7,10,7,10,7,
%T 11,8,12,9,13,10,15,12,17,14,19,15,20,16,21,17,22,18,24,19,25,20,26,
%U 21,28,23,30,25,32,27,34,29,36,31,38,32,40,34,42,36
%N Number of integer-sided triangles with perimeter n whose smallest side length is prime.
%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(k), where c(n) is the prime characteristic (A010051).
%t Table[Sum[Sum[ (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.
%K nonn
%O 1,9
%A _Wesley Ivan Hurt_, May 27 2019
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