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Coresilience

Problem 245

Published on Friday, 15th May 2009, 02:00 pm; Solved by 527

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) = 411.

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)
1

p - 1
.

Find the sum of all composite integers 1 < n ≤ 2×1011, for which C(n) is a unit fraction.