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%I #8 Jun 18 2020 13:59:07
%S 0,0,1,0,1,1,2,1,2,1,2,1,3,3,6,5,7,6,7,5,7,5,7,5,7,6,9,8,12,12,16,15,
%T 19,17,21,19,23,21,26,23,27,25,29,26,31,28,33,30,35,32,37,33,38,35,40,
%U 37,42,39,44,41,47,45,52,49,55,52,58,54,61,57,64,60
%N Number of integer-sided triangles with perimeter n and side lengths a, b and c such that a <= b <= c, and b is squarefree.
%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))) * mu(i)^2, where mu is the Möbius function (A008683).
%t Table[Sum[Sum[ MoebiusMu[i]^2* Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
%Y Cf. A008683, A308454.
%K nonn
%O 1,7
%A _Wesley Ivan Hurt_, May 27 2019
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