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%I #10 May 12 2019 14:21:09
%S 24,88,280,472,558,664,696,852,856,1048,1432,1720,1816,2008,2180,2292,
%T 2680,2776,2868,3144,3352,3544,3576,3582,3732,3736,3860,3928,4192,
%U 4308,4504,4696,4878,4976,5080,5172,5272,5464,5598,5748,6520,6616,6740,6744,7188
%N Numbers that are the perimeter of a Heronian triangle, but not of a primitive Heronian triangle.
%C Numbers in A051518 that are not in A096468.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>
%e The only Heronian triangle with perimeter 24 has sides {6, 8, 10} and thus it is not primitive. Hence 24 is in the sequence.
%t hpp[p_] := Catch@Block[{t=0, c, q=p/2}, Do[c = p-a-b; If[c >= b && a+c > b && a+b > c && IntegerQ@ Sqrt[q (q-a) (q-b) (q-c)], t++; If[GCD[a, b, c] == 1, Throw@ False]], {a, p/3}, {b, a, p-a-1}]; t > 0]; Select[2 Range[350], hpp]
%Y Cf. A051518, A096468.
%K nonn
%O 1,1
%A _Giovanni Resta_, Jun 14 2018
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