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

2, 0, 9, 81, 189, 441, 1449, 10206, 3969, 12789, 13041, 35721, 30429, 194481, 117369, 115101, 186921, 2893401, 273861

Offset: 0

Author

Seiichi Manyama, Jul 02 2024

Keywords

• nonn
• more

Comments

For n > 1, a(n) is the smallest nonnegative k such that A216283(k) = n.

a(20) = 378189.

a(21) = 1035909.

a(22) = 9506889.

a(23) = 2099601.

a(24) = 882441.

a(25) = 5639949.

a(26) = 85562001.

a(27) = 6765381.

a(28) = 3403701.

a(30) = 3925341.

a(32) = 5420709.

a(33) = 83908629.

a(35) = 50759541.

a(36) = 7941969.

a(38) = 102880449.

a(40) = 15505749.

a(41) = 170067681.

a(42) = 35328069.

Crossrefs

Cf. A374285, A374286.

Cf. A216283.

Programs

PARI

b(n, k) = sum(i=0, sqrtint(n), sum(j=0, sqrtint(n\k), i^2+k*j^2==n));
a(n, k=5) = my(cnt=0); while(b(cnt, k)!=n, cnt++); cnt;