This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A070103 #11 May 14 2019 10:21:45 %S A070103 0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,2,0,1,0,0,0,0,0, %T A070103 2,0,1,0,3,0,2,0,2,0,1,0,3,0,2,0,1,0,2,0,0,0,0,0,3,0,1,0,4,0,5,0,4,0, %U A070103 2,0,1,0,1,0,2,0,2,0,3,0,1,0,6,0,4,0,6,0,6,0 %N A070103 Number of obtuse integer triangles with perimeter n and prime side lengths. %H A070103 R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a> %F A070103 a(n) = A070093(n) - A070098(n). %F A070103 a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1 - sign(floor((i^2 + k^2)/(n-i-k)^2))) * sign(floor((i + k)/(n-i-k+1))) * A010051(i) * A010051(k) * A010051(n-i-k). - _Wesley Ivan Hurt_, May 13 2019 %e A070103 For n=11 there are A005044(11)=4 integer triangles: [1,5,5], [2,4,5], [3,3,5] and [3,4,4]; only one of the two obtuses ([2,4,5] and [3,3,5]) consists of primes, therefore a(11)=1. %t A070103 Table[Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[n - i - k] - PrimePi[n - i - k - 1]) (1 - Sign[Floor[(i^2 + k^2)/(n - i - k)^2]]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}] (* _Wesley Ivan Hurt_, May 13 2019 *) %Y A070103 Cf. A070080, A070081, A070082, A070093, A070098, A070101, A070088, A070105, A070108, A070129. %K A070103 nonn %O A070103 1,27 %A A070103 _Reinhard Zumkeller_, May 05 2002