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%I #32 Aug 06 2017 14:35:29
%S 24,84,192,336,540,756,1134,1344,1710,2100,2640,3000,4056,4116,4680,
%T 5376,6936,6804,8664,8400,9240,10164,12696,12000,13500,14196,15390,
%U 16296,20184,18720,23064,21504,23232,24276,26040,27000,32856,30324
%N Smallest area of triangle with integer sides and area = n times perimeter.
%H Ray Chandler, <a href="/A289155/b289155.txt">Table of n, a(n) for n = 1..5000</a> (first 300 terms from Zhining Yang)
%F a(n) = A120572(2n). - _Ray Chandler_, Jul 27 2017
%e For n = 4, a(4)=336 means for the smallest triangle (a,b,c) = (26,28,30), the area is 336, which is 4 times the perimeter 84.
%o (PARI) for(k=1, 50, n=0;A=10^9; d=4*k^2; e=3*d; for(b=1, sqrt(e), for (c=2*k, e/b, if(b*c>d&&c>=b, f = (b + c)*d / (b * c - d); if(f>=c, a=floor(f); if(a==f, n++; s=2*(a+b+c)*k;if(s<A,A=s)))))); print1(A, ", "))
%Y Cf. A007237, A120572, A188158, A228383.
%Y a(n) is the leading entry in row n of the triangle in A290451.
%K nonn
%O 1,1
%A _Zhining Yang_, Jun 26 2017
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