Project Euler #245: Coresilience

_{This problem is a programming version of Problem 245 from projecteuler.net}

We shall call a fraction that cannot be cancelled down a resilient fraction.

Furthermore we shall define the resilience of a denominator, , to be the ratio of its proper fractions that are resilient; for example, consider . The proper fractions with a denominator are . Four of these cannot be cancelled down, so the resilience is .

The resilience of a number is then

where φ is Euler's totient function.

We further define the coresilience of a number

Given an integer , find the sum of all integers for which is a unit fraction, that is, a fraction with a numerator of after cancelling down.

Input Format

Each test file contains a single line containing a single integer .

Constraints

Output Format

Print the integer value of the sum of all integers for which is a unit fraction.

Sample Input 0

Sample Output 0

Explanation 0

Integer	2	3	4	5
Euler Phi	1	2	2	4
Coresilience	1/1	1/2	2/3	1/4

The sum of integers with Coresilience a unit fraction: .