A169618 Table with T(n,k) = the number of ways to represent k as the sum of a square and a cube modulo n.

1, 2, 2, 3, 3, 3, 6, 6, 2, 2, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 11, 8, 12, 2, 6, 3, 12, 20, 4, 4, 12, 4, 4, 4, 15, 15, 6, 6, 6, 6, 6, 6, 15, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 18, 18, 6, 6, 18, 18, 6, 6, 18, 18, 6, 6, 13, 11, 18, 8, 20, 15, 6

Offset: 1

Author

Franklin T. Adams-Watters, Dec 03 2009

Keywords

• nonn
• tabl

Comments

The top left corner is T(1,0).

It appears that this table does not contain any 0's.

It appears that row n is constant iff n is squarefree, and no prime divisor of n is == 1 (mod 6). It is not hard to show that such rows are constant, since the cubes are equi-distributed in such moduli.

Examples

			The 6 ways to represent 0 (mod 4) are 0^2+0^3, 0^2+2^3, 1^2+3^3, 2^2+0^3, 2^2+2^3, and 3^2+3^3.
		

Crossrefs

Cf. A022549, A002476, A045309.

Programs

PARI

al(n)=local(v);v=vector(n);for(i=0,n-1,for(j=0,n-1,v[(i^2+j^3)%n+1]++));v