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%I #8 Aug 15 2020 12:25:32
%S 3,6,9,10,12,13,15,18,20,21,24,26,27,28,30,31,33,35,36,37,39,40,42,45,
%T 46,47,48,50,51,52,53,54,55,56,57,60,61,62,63,64,65,66,69,70,71,72,73,
%U 74,75,77,78,80,81,84,85,86,87,89,90,91,92,93,94,96,97,98,99,100,101,102,104
%N Perimeters of integer-sided triangles such that the harmonic mean of their side lengths is an integer.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%e 6 is in the sequence since the integer-sided triangle [2,2,2] (with perimeter 6) has harmonic mean 3*2*2*2/(2*2+2*2+2*2) = 2 (an integer).
%e 10 is in the sequence since the triangle [2,4,4] (with perimeter 10) has harmonic mean 3*2*4*4/(2*4+2*4+4*4) = 96/32 = 3 (an integer).
%t Table[If[Sum[Sum[(1 - Ceiling[3*i*k*(n - i - k)/(i*k + k*(n - i - k) + i*(n - i - k))] + Floor[3*i*k*(n - i - k)/(i*k + k*(n - i - k) + i*(n - i - k))]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 100}] // Flatten
%Y Cf. A337086.
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Aug 14 2020
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