--description--

Consider equations of the form: $a^2 + b^2 = N$, $0 ≤ a ≤ b$, $a$, $b$ and $N$ integer.

For $N = 65$ there are two solutions:

$a = 1, b = 8$ and $a = 4, b = 7$.

We call $S(N)$ the sum of the values of $a$ of all solutions of $a^2 + b^2 = N$, $0 ≤ a ≤ b$, $a$, $b$ and $N$ integer.

Thus $S(65) = 1 + 4 = 5$.

Find $\sum S(N)$, for all squarefree $N$ only divisible by primes of the form $4k + 1$ with $4k + 1 < 150$.

--hints--

sumOfSquares() should return 2032447591196869000.

assert.strictEqual(sumOfSquares(), 2032447591196869000);

--seed--

--seed-contents--

function sumOfSquares() {

  return true;
}

sumOfSquares();

--solutions--

// solution required