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 positive integers n 10^{18} for which p(n) has the form k + ^{1}⁄_{2}, where k is an integer.
These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK