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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 A374161 #18 Jul 01 2024 13:09:39
%S A374161 0,20,140,700,1540,17500,7700,122500,26180,53900,192500,7035875,
%T A374161 130900,592900,4812500,1347500,602140,150062500,916300
%N 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.
%o A374161 (Python)
%o A374161 from itertools import count
%o A374161 from sympy.abc import x,y
%o A374161 from sympy.solvers.diophantine.diophantine import diop_quadratic
%o A374161 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 A374161 Cf. A328151, A343105, A374158, A374159, A374160.
%K A374161 nonn,more
%O A374161 0,2
%A A374161 _Seiichi Manyama_, Jun 29 2024