A374161 a(n) is the smallest nonnegative integer k where exactly n pairs of positive integers (x, y) exist such that x^2 + 19*y^2 = k.
0, 20, 140, 700, 1540, 17500, 7700, 122500, 26180, 53900, 192500, 7035875, 130900, 592900, 4812500, 1347500, 602140, 150062500, 916300
Offset: 0
Programs
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Python
from itertools import count from sympy.abc import x,y from sympy.solvers.diophantine.diophantine import diop_quadratic def A374161(n): return next(m for m in count(0) if sum(1 for d in diop_quadratic(x**2+19*y**2-m) if d[0]>0 and d[1]>0)==n) # Chai Wah Wu, Jun 30 2024