Here :
http://mathworld.wolfram.com/SumofSquaresFunction.html
$r_2'(n)$ is a function calculating the number of solutions $a^2+b^2=n$ with integers $a,b$ satisfying $0<a\le b$
How can I calculate $P(n)$ , which shall be here the number of the primitive solutions ($\gcd(a,b)=1$) of $a^2+b^2=n$ with integers $a,b$ satisfying $0<a\le b$ ?
Some cases are relatively easy :
- If $n$ is odd and squarefree, $\gcd(a,b)$ is necessarily satisfied. Hence we just have $P(n)=r_2'(n)$
- If $n$ is an odd square of a squarefree number $m$ , then it can be shown that $P(n)=P(m)$ holds.
But how can I calculate $P(n)$ in general ?