

A239434


Number of nonnegative integer solutions to the equation x^2  25*y^2 = n.


2



1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,64


COMMENTS

For (x, y) to be a solution to the more general equation x^2  d^2*y^2 = n, it can be shown that nf^2 must be divisible by 2*f*d, where f is a divisor of n not exceeding sqrt(n). Then y = (nf^2)/(2*f*d) and x = d*y+f.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000


EXAMPLE

a(64)=2 because x^2  25*y^2 = 64 has two solutions, (X,Y) = (8,0) and (17,3).


PROG

(PARI) a(n) = sumdiv(n, f, f^2<=n && (nf^2)%(10*f)==0)


CROSSREFS

Cf. A034178, A230240, A230263, A230264, A239435.
Sequence in context: A291147 A278929 A277143 * A033770 A216283 A262900
Adjacent sequences: A239431 A239432 A239433 * A239435 A239436 A239437


KEYWORD

nonn


AUTHOR

Colin Barker, Mar 18 2014


STATUS

approved



