Problem 241Published on Saturday, 18th April 2009, 02:00 am; Solved by 572; Difficulty rating: 80%
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)||=||
Find the sum of all positive integers n ≤ 1018 for which p(n) has the form k + 1⁄2, where k is an integer.