A374159 a(n) is the smallest nonnegative integer k where exactly n pairs of positive integers (x, y) exist such that x^2 + 7*y^2 = k.

0, 8, 32, 128, 352, 704, 1408, 2816, 5632, 11264, 16192, 45056, 32384, 123904, 64768, 178112, 129536, 2883584, 259072, 1982464, 469568, 712448, 1036288, 184549376, 939136, 21551552, 4145152, 2849792, 1878272

Offset: 0

Author

Seiichi Manyama, Jun 29 2024

Keywords

• nonn
• more

Comments

a(n) is the smallest nonnegative k such that A216511(k) = n.

Conjecture: All terms are multiple of a(1) = 8.

a(30) = 5165248.

a(31) = 16386304.

a(32) = 3756544.

a(33) = 11399168.

a(34) = 66322432.

a(35) = 86206208.

a(36) = 7513088.

Crossrefs

Cf. A328151, A343105, A374158, A374160, A374161.

Cf. A216511.

Programs

Python

from itertools import count
from sympy.abc import x, y
from sympy.solvers.diophantine.diophantine import diop_quadratic
def A374159(n): return next(m for m in count(0) if sum(1 for d in diop_quadratic(x**2+7*y**2-m) if d[0]>0 and d[1]>0)==n) # Chai Wah Wu, Jun 30 2024