id	title	challengeType	forumTopicId	dashedName
5900f45d1000cf542c50ff70	Problem 241: Perfection Quotients	5	301888	problem-241-perfection-quotients

--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);

function perfectionQuotients() {

  return true;
}

perfectionQuotients();

// solution required