A289155 Smallest area of triangle with integer sides and area = n times perimeter.

24, 84, 192, 336, 540, 756, 1134, 1344, 1710, 2100, 2640, 3000, 4056, 4116, 4680, 5376, 6936, 6804, 8664, 8400, 9240, 10164, 12696, 12000, 13500, 14196, 15390, 16296, 20184, 18720, 23064, 21504, 23232, 24276, 26040, 27000, 32856, 30324

Offset: 1

Author

Zhining Yang, Jun 26 2017

Keywords

• nonn

Examples

			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.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..5000 (first 300 terms from Zhining Yang)

Crossrefs

Cf. A007237, A120572, A188158, A228383.

a(n) is the leading entry in row n of the triangle in A290451.

Programs

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
				

Formula

a(n) = A120572(2n). - Ray Chandler, Jul 27 2017