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
where φ is Euler's totient function.
We further define the
of a number
Given an integer , find the sum of all integers
is a unit fraction, that is, a fraction with a numerator of after cancelling down.
Each test file contains a single line containing a single integer .
Print the integer value of the sum of all integers
is a unit fraction.
Sample Input 0
Sample Output 0
The sum of integers with Coresilience a unit fraction: .