OFFSET
1,1
COMMENTS
The sequence gives the sorted areas of primitive triangles which have integer side lengths and integer areas.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
Michael Somos, Heronian Triangle Table
EXAMPLE
The smallest Heronian triangle is (3,4,5) as perimeter and area are integers. The first term of the sequence is thus the area of this triangle, which is 6.
MATHEMATICA
AMax=400;
Do[
c=p/b;
a1=Sqrt[b^2+c^2+2Sqrt[b^2c^2-4A^2]];
a2=Sqrt[b^2+c^2-2Sqrt[b^2c^2-4A^2]];
If[IntegerQ[a2]&&GCD[a2, b, c]==1&&a1>a2>=b, A//Sow(*{A, a2, b, c}//Sow*)];
If[IntegerQ[a1]&&GCD[a1, b, c]==1, A//Sow(*{A, a1, b, c}//Sow*)];
, {A, 6, AMax, 6}
, {p, 4A^2//Divisors//Select[#, EvenQ[#]&&#>=2A&]&//#/2+2A^2/#&//Select[#, IntegerQ]&}
, {b, p//Divisors//Select[#, #^2>=p&]&}
]//Reap//Last//Last
{a1, a2, c}=.;
(* Albert Lau, May 20 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Mihir Mathur, Apr 03 2013
EXTENSIONS
Definition corrected by Giovanni Resta, Apr 03 2013
More terms from Giovanni Resta, Apr 03 2013
STATUS
approved