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%I #7 Jun 18 2020 13:52:31
%S 0,0,1,0,0,0,0,0,4,0,0,4,6,4,0,6,8,12,15,14,24,31,17,35,38,45,27,49,
%T 42,71,64,76,92,118,73,117,110,149,97,146,121,194,170,217,240,294,184,
%U 277,249,339,349,389,381,502,514,566,618,693,538,658,672,764
%N Take all the integer-sided triangles with perimeter n and nonprime sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b's.
%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))) * A005171(i) * A005171(k) * A005171(n-i-k) * i.
%t Table[Sum[Sum[i*(1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[k] + PrimePi[k - 1]) (1 - PrimePi[n - i - k] + PrimePi[n - i - k - 1]) Sign[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 1,9
%A _Wesley Ivan Hurt_, May 17 2019
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