

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



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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



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 equidistributed 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, n1, for(j=0, n1, 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. AdamsWatters, Dec 03 2009


STATUS

approved



