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Coresilience
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) = 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) | = | 1 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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