--description--

For a positive integer $n$, let $σ(n)$ be the sum of all divisors of $n$, so e.g. $σ(6) = 1 + 2 + 3 + 6 = 12$.

A perfect number, as you probably know, is a number with $σ(n) = 2n$.

Let us define the perfection quotient of a positive integer as $p(n) = \frac{σ(n)}{n}$.

Find the sum of all positive integers $n ≤ {10}^{18}$ for which $p(n)$ has the form $k + \frac{1}{2}$, where $k$ is an integer.

--hints--

perfectionQuotients() should return 482316491800641150.

assert.strictEqual(perfectionQuotients(), 482316491800641150);

--seed--

--seed-contents--

function perfectionQuotients() {

  return true;
}

perfectionQuotients();

--solutions--

// solution required