Project Euler/241

Problem Statement

Perfection Quotients

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) = σ(n)/n.

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