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A374160 a(n) is the smallest nonnegative integer k where exactly n pairs of positive integers (x, y) exist such that x^2 + 11*y^2 = k.

%I A374160 #22 Jul 01 2024 15:26:55
%S A374160 0,12,60,180,540,1620,2700,8100,12420,20700,37260,1180980,62100,
%T A374160 476100,335340,186300,310500,1822500,558900,53144100,931500,1676700,
%U A374160 4284900,324860625,1925100,4657500,244462860,12854700,8383500
%N A374160 a(n) is the smallest nonnegative integer k where exactly n pairs of positive integers (x, y) exist such that x^2 + 11*y^2 = k.
%C A374160 a(n) is the smallest nonnegative k such that A374017(k) = n.
%C A374160 a(30) = 5775300.
%C A374160 a(31) = 38564100.
%C A374160 a(32) = 9625500.
%C A374160 a(33) = 135812700.
%C A374160 a(35) = 41917500.
%C A374160 a(36) = 17325900.
%C A374160 a(37) = 107122500.
%C A374160 a(40) = 28876500.
%o A374160 (Python)
%o A374160 from itertools import count
%o A374160 from sympy.abc import x,y
%o A374160 from sympy.solvers.diophantine.diophantine import diop_quadratic
%o A374160 def A374160(n): return next(m for m in count(0) if sum(1 for d in diop_quadratic(x**2+11*y**2-m) if d[0]>0 and d[1]>0)==n) # _Chai Wah Wu_, Jun 30 2024
%Y A374160 Cf. A328151, A343105, A374158, A374159, A374161.
%Y A374160 Cf. A374017.
%K A374160 nonn,more
%O A374160 0,2
%A A374160 _Seiichi Manyama_, Jun 29 2024