A173636 - OEIS

%I #19 Oct 12 2018 12:14:14

%S 0,0,0,1,0,1,1,1,1,2,1,1,1,1,1,4,2,1,2,1,1,4,1,1,4,2,1,3,1,1,4,1,3,4,

%T 1,4,2,1,1,4,4,1,4,1,1,7,1,1,7,2,2,4,1,1,3,4,4,4,1,1,4,1,1,7,4,4,4,1,

%U 1,4,4,1,7,1,1,7,1,4,4

%N Number of positive solutions of equation x(x+n)=y*y.

%C The solution x=y=0 is not counted.

%C Same as A115878 except for a(0). - _Georg Fischer_, Oct 12 2018

%F a(n) = A176835(n)-1. - _R. J. Mathar_, Nov 23 2010

%e a(9)=2 since x(x+9)=y*y has 2 solutions: x=3, y=6 and x=16, y=20.

%t Join[{0}, Table[Length[{ToRules[Reduce[x (x + n) == y^2 && x > 0 && y > 0, {x, y}, Integers]]}], {n, 100}]]

%Y Cf. A067721, A115878.

%K nonn

%O 0,10

%A _Carmine Suriano_, Nov 23 2010