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

1,2

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.

Links

Table of n, a(n) for n=1..85.

Example

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.

Prog

(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

Crossrefs

Cf. A022549, A002476, A045309.

Sequence in context: A239518 A293924 A307730 * A175454 A157501 A080968

Adjacent sequences: A169615 A169616 A169617 * A169619 A169620 A169621

Keyword

nonn,tabl

Author

Franklin T. Adams-Watters, Dec 03 2009

Status

approved