A383766 a(n) is the number of numbers k (0 <= k < n) such that there exist solutions of x^3 + x == y^2 + 1 == k (mod n).

1, 1, 2, 1, 2, 2, 3, 1, 4, 2, 3, 2, 6, 3, 4, 2, 5, 4, 7, 2, 6, 3, 8, 2, 10, 6, 11, 3, 12, 4, 11, 4, 6, 5, 6, 4, 13, 7, 12, 2, 11, 6, 16, 3, 8, 8, 13, 4, 21, 10, 10, 6, 17, 11, 6, 3, 14, 12, 18, 4, 20, 11, 12, 8, 12, 6, 27, 5, 16, 6, 26, 4, 27, 13, 20, 7, 9, 12, 26, 4, 31, 11, 25

Offset: 1

Author

SiYang Hu, May 09 2025

Keywords

• nonn

Examples

			a(7) = 3: k can be 2, 3, 5, for example, when k = 3, x = 2, and y = 4, the equation is satisfied.
		

Links

• SiYang Hu, Table of n, a(n) for n = 1..10000

Programs

Mathematica

A383766 = Table[Count[Range[0, n - 1], k_ /; Length[Solve[{x^3 + x == k, y^2 + 1 == k}, {x, y}]] > 0], {n, 1, 50}];

Formula

If 8 does not divide n, a(2n) = a(n).

If 8 divides n, a(2n) = 2*a(n).