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A374286 a(n) is the smallest nonnegative integer k where there are exactly n nonnegative integer solutions to x^2 + 3*y^2 = k.

%I A374286 #16 Jul 03 2024 08:34:30
%S A374286 2,0,4,28,1729,196,364,1529437,9604,2548,593047,470596,6916,68574961,
%T A374286 33124,124852,1983163
%N A374286 a(n) is the smallest nonnegative integer k where there are exactly n nonnegative integer solutions to x^2 + 3*y^2 = k.
%C A374286 a(n) is the smallest nonnegative k such that A119395(k) = n.
%C A374286 a(18) = 48412.
%C A374286 a(20) = 18384457.
%C A374286 a(21) = 6117748.
%C A374286 a(23) = 1623076.
%C A374286 a(24) = 214396.
%C A374286 a(27) = 629356.
%C A374286 a(30) = 2372188.
%C A374286 a(32) = 79530724.
%C A374286 a(36) = 1500772.
%C A374286 a(41) = 11957764.
%C A374286 a(42) = 116237212.
%o A374286 (PARI) b(n, k) = sum(i=0, sqrtint(n), sum(j=0, sqrtint(n\k), i^2+k*j^2==n));
%o A374286 a(n, k=3) = my(cnt=0); while(b(cnt, k)!=n, cnt++); cnt;
%Y A374286 Cf. A374285, A374288.
%Y A374286 Cf. A119395, A374158.
%K A374286 nonn,more
%O A374286 0,1
%A A374286 _Seiichi Manyama_, Jul 02 2024