A374161 - OEIS

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.

%I #18 Jul 01 2024 13:09:39

%S 0,20,140,700,1540,17500,7700,122500,26180,53900,192500,7035875,

%T 130900,592900,4812500,1347500,602140,150062500,916300

%N 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.

%o (Python)

%o from itertools import count

%o from sympy.abc import x,y

%o from sympy.solvers.diophantine.diophantine import diop_quadratic

%o 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

%Y Cf. A328151, A343105, A374158, A374159, A374160.

%K nonn,more

%O 0,2

%A _Seiichi Manyama_, Jun 29 2024