A082523 Number of times k^2 + (n-k)^2 is a square for 1 <= k <= n-1.

0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0

Offset: 2

Author

CHAUVIN thierry (thierry.chauvin2(AT)wanadoo.fr), Apr 30 2003

Keywords

• nonn

Comments

a(n) is not zero for n = 7, 14, 17, 21, 23, 28, ... : A118905. - Michel Marcus, Jun 09 2013

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A118905.

Programs

Magma

[#[k:k in [1..n-1]|IsSquare(k^2+(n-k)^2)]:n in [2..90]]; // Marius A. Burtea, Jul 29 2019

Mathematica

Table[Total[Boole[IntegerQ[Sqrt[#]]&/@Table[k^2+(n-k)^2,{k,n-1}]]],{n,2,90}] (* Harvey P. Dale, Aug 15 2017 *)

PARI

a(n) = sum(k=1, n-1, issquare(k^2+(n-k)^2)) \\ Michel Marcus, Jun 09 2013

Extensions

Edited and extended by Michel Marcus, Jun 09 2013