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%I #10 Jun 16 2020 13:11:20
%S 0,0,1,0,0,0,0,0,1,0,0,1,1,1,0,1,1,2,2,2,3,4,2,4,4,5,3,5,4,7,6,7,8,10,
%T 6,9,8,11,7,10,8,13,11,14,15,18,11,16,14,19,19,21,20,26,26,28,30,33,
%U 25,30,30,34,27,32,29,37,35,39,40,45,44,47,47,53
%N Number of integer-sided triangles with perimeter n and nonprime side lengths.
%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))) * c(i) * c(k) * c(n-i-k), where c(n) = A005171(n).
%t Table[Sum[Sum[(1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[k] + PrimePi[k - 1]) (1 - PrimePi[n - i - k] + PrimePi[n - i - k - 1]) Sign[
%t Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
%Y Cf. A005171.
%K nonn
%O 1,18
%A _Wesley Ivan Hurt_, May 17 2019
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