Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Jun 16 2020 14:34:53
%S 0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,4,4,4,0,8,12,8,9,12,8,9,0,8,17,
%T 9,0,24,9,12,9,24,18,24,9,44,18,20,9,48,18,36,17,77,33,59,36,83,70,67,
%U 65,123,88,63,81,111,92,89,74,169,75,90,66,154
%N Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose sides are nonsquarefree.
%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))) * (1 - mu(i)^2) * (1 - mu(k)^2) * (1 - mu(n-i-k)^2) * k, where mu is the Möbius function (A008683).
%t Table[Sum[Sum[k (1 - MoebiusMu[i]^2)*(1 - MoebiusMu[k]^2)*(1 - MoebiusMu[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. A008683, A308424.
%K nonn
%O 1,12
%A _Wesley Ivan Hurt_, May 26 2019