--description--

A unitary divisor $d$ of a number $n$ is a divisor of $n$ that has the property $gcd(d, \frac{n}{d}) = 1$.

The unitary divisors of $4! = 24$ are 1, 3, 8 and 24.

The sum of their squares is $12 + 32 + 82 + 242 = 650$.

Let $S(n)$ represent the sum of the squares of the unitary divisors of $n$. Thus $S(4!) = 650$.

Find $S(100\,000\,000!)$ modulo $1\,000\,000\,009$.

--hints--

sumSquaresOfUnitaryDivisors() should return 98792821.

assert.strictEqual(sumSquaresOfUnitaryDivisors(), 98792821);

--seed--

--seed-contents--

function sumSquaresOfUnitaryDivisors() {

  return true;
}

sumSquaresOfUnitaryDivisors();

--solutions--

// solution required