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A374288 a(n) is the smallest nonnegative integer k where there are exactly n nonnegative integer solutions to x^2 + 5*y^2 = k.

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%I A374288 #11 Jul 03 2024 08:34:34
%S A374288 2,0,9,81,189,441,1449,10206,3969,12789,13041,35721,30429,194481,
%T A374288 117369,115101,186921,2893401,273861
%N A374288 a(n) is the smallest nonnegative integer k where there are exactly n nonnegative integer solutions to x^2 + 5*y^2 = k.
%C A374288 For n > 1, a(n) is the smallest nonnegative k such that A216283(k) = n.
%C A374288 a(20) = 378189.
%C A374288 a(21) = 1035909.
%C A374288 a(22) = 9506889.
%C A374288 a(23) = 2099601.
%C A374288 a(24) = 882441.
%C A374288 a(25) = 5639949.
%C A374288 a(26) = 85562001.
%C A374288 a(27) = 6765381.
%C A374288 a(28) = 3403701.
%C A374288 a(30) = 3925341.
%C A374288 a(32) = 5420709.
%C A374288 a(33) = 83908629.
%C A374288 a(35) = 50759541.
%C A374288 a(36) = 7941969.
%C A374288 a(38) = 102880449.
%C A374288 a(40) = 15505749.
%C A374288 a(41) = 170067681.
%C A374288 a(42) = 35328069.
%o A374288 (PARI) b(n, k) = sum(i=0, sqrtint(n), sum(j=0, sqrtint(n\k), i^2+k*j^2==n));
%o A374288 a(n, k=5) = my(cnt=0); while(b(cnt, k)!=n, cnt++); cnt;
%Y A374288 Cf. A374285, A374286.
%Y A374288 Cf. A216283.
%K A374288 nonn,more
%O A374288 0,1
%A A374288 _Seiichi Manyama_, Jul 02 2024