

A289155


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


5



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
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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



