Problem 245

Published on 15 May 2009 at 02:00 pm [Server Time]

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
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)
p − 1

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

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