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A374285 a(n) is the smallest nonnegative integer k where there are exactly n nonnegative integer solutions to x^2 + 2*y^2 = k.

%I A374285 #18 Jul 03 2024 08:34:38
%S A374285 5,0,9,81,297,891,1683,8019,5049,18513,15147,88209,31977,1185921,
%T A374285 136323,166617,95931,7144929,351747
%N A374285 a(n) is the smallest nonnegative integer k where there are exactly n nonnegative integer solutions to x^2 + 2*y^2 = k.
%C A374285 For n > 1, a(n) is the smallest nonnegative k such that A216282(k) = n.
%C A374285 a(20) = 287793.
%C A374285 a(21) = 1499553.
%C A374285 a(22) = 11042163.
%C A374285 a(23) = 2832489.
%C A374285 a(24) = 863379.
%C A374285 a(25) = 20160657.
%C A374285 a(26) = 99379467.
%C A374285 a(27) = 5979699.
%C A374285 a(28) = 2590137.
%C A374285 a(30) = 3165723.
%C A374285 a(32) = 3933171.
%C A374285 a(33) = 121463793.
%C A374285 a(35) = 181445913.
%C A374285 a(36) = 9497169.
%o A374285 (PARI) b(n, k) = sum(i=0, sqrtint(n), sum(j=0, sqrtint(n\k), i^2+k*j^2==n));
%o A374285 a(n, k=2) = my(cnt=0); while(b(cnt, k)!=n, cnt++); cnt;
%Y A374285 Cf. A374286, A374288.
%Y A374285 Cf. A200977, A216282, A374294.
%K A374285 nonn,more
%O A374285 0,1
%A A374285 _Seiichi Manyama_, Jul 02 2024