OFFSET
1,1
COMMENTS
This sequence lists the sums a+b+c of the triples of sides (a,b,c) of A357274.
Also, sum a+b+c of the solutions of the Diophantine equation c^2 = a^2 + a*b + b^2 with gcd(a,b) = 1 and a < b.
For miscellaneous properties, links and references, see A357274.
This sequence is not increasing. For example, a(23) = 350 for triangle with longest side = 163 while a(24) = 345 for triangle with longest side = 169.
FORMULA
EXAMPLE
(3, 5, 7) is the smallest triple in A357274 with 7^2 = 3^2 + 3*5 + 5^2, so a(1) = 3 + 5 + 7 = 15.
MAPLE
for c from 5 to 100 by 2 dofor a from 3 to c-2 do
b := (-a + sqrt(4*c^2-3*a^2))/2;
if b=floor(b) and gcd(a, b)=1 and a<b then print(a+b+c); end if;
end do;
end do;
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Oct 24 2022
STATUS
approved