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

1,1

Links

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

Formula

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

Example

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.

Prog

(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, ", "))

Crossrefs

Cf. A007237, A120572, A188158, A228383.

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

Sequence in context: A304158 A045946 A192838 * A101861 A280304 A168538

Adjacent sequences: A289152 A289153 A289154 * A289156 A289157 A289158

Keyword

nonn

Author

Zhining Yang, Jun 26 2017

Status

approved