Problem 245
Coresilience
We shall call a fraction that cannot be cancelled down a resilient fraction. Furthermore we shall define the resilience of a denominator, R(d), to be the ratio of its proper fractions that are resilient; for example, R(12) = 4⁄11.
The resilience of a number d > 1 is then$\frac{\phi(d)}{d-1}$ where φ is Euler’s totient function.
We further define the coresilience of a number n > 1 as C(n)=$\frac{n − \phi(n)}{n-1}$.
The coresilience of a prime p is C(p)=$\frac{1}{p-1}$.
Find the sum of all composite integers 1 < n ≤ 2×1011, for which C(n) is a unit fraction.
可约度
我们称不能被约简的分数为不可约分数。进一步地，我们可以定义分母的不可约度R(d)为它的真分数中不可约分数的比例；例如，R(12) = 4/11。
数d > 1的不可约度可以表示成$\frac{\phi(d)}{d-1}$，其中φ是欧拉总计函数。
我们进一步定义数n > 1的可约度为C(n)=$\frac{n − \phi(n)}{n-1}$。
素数p的可约度为C(p)=$\frac{1}{p-1}$。
在所有1 < n ≤ 2×1011的合数中，有些数满足C(n)约简后为单位分数，求这些数之和。