A173636 Number of positive solutions of equation x(x+n)=y*y.

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, 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, 1, 4, 4, 1, 7, 1, 1, 7, 1, 4, 4

Offset

0,10

Comments

The solution x=y=0 is not counted.

Same as A115878 except for a(0). - Georg Fischer, Oct 12 2018

Links

Table of n, a(n) for n=0..78.

Formula

a(n) = A176835(n)-1. - R. J. Mathar, Nov 23 2010

Example

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

Mathematica

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

Crossrefs

Cf. A067721, A115878.

Sequence in context: A326851 A129192 A062540 * A115878 A127125 A256671

Adjacent sequences: A173633 A173634 A173635 * A173637 A173638 A173639

Keyword

nonn

Author

Carmine Suriano, Nov 23 2010

Status

approved