OFFSET
1,1
COMMENTS
I have verified that for all integers n <= 10000, there always exist triples (x,y,z) of positive integers such that x^3 + n*x*y + y^3 = z^3.
For example: n=4459, (2835, 14700, 15015) is a solution.
EXAMPLE
a(3)=26 because there exists a triple (14,24,26) satisfying 14^3 + 3*14*24 + 24^3 = 26^3, and no smaller solution exists.
MATHEMATICA
Table[First[
Sort@Flatten[
Table[CubeRoot[x^3 + n*x*y + y^3], {x, 1, 400}, {y, x + 1, 400}]],
IntegerQ[#] &], {n, 1, 30}]
PROG
(Python)
def a(n):
r=400
for x in range(1, 400):
for y in range(x+1, 400):
zz=x**3+n*x*y+y**3
z=round(zz**(1/3))
if zz==z**3 and z<r:
r=z
return(r)
print([a(n) for n in range(1, 31)])
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhining Yang, Mar 11 2023
EXTENSIONS
More terms from Sean A. Irvine, Apr 10 2023
STATUS
approved