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%I #15 Sep 05 2021 18:27:13
%S 24,30,32,36,40,42,44,56,60,64,76,80,84,96,104,108,120,132,140,144,
%T 156,168,192,204,216,220,228,240,252,276,288,312,324,336,348,360,372,
%U 396,408,420,444,480,492,516,528,552,564,576,588,624,636,660,672,684,708,732
%N Perimeters of integer-sided triangles with prime inradius.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Incircle.html">Incircle</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle">Incircle and excircles of a triangle</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%t Flatten[Table[If[Sum[Sum[(PrimePi[Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/(n/2)] - PrimePi[Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/(n/2) - 1]) (1 - Ceiling[Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/(n/2)] + Floor[Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/(n/2)]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 100}]]
%Y Cf. A005044, A333945 (integer inradius).
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Apr 11 2020
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