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
φ(d)d − 1
, where φ is Euler's totient function.
We further define the coresilience of a number n > 1 as C(n)=
n − φ(n)n − 1.
The coresilience of a prime p is C(p)
=
1p − 1.
Find the sum of all composite integers 1 <n≤2×1011,forwhichC(n)isaunitfraction.