Problem 245Published on Friday, 15th May 2009, 02:00 pm; Solved by 524; Difficulty rating: 80%
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||
|, where φ is Euler's totient function.|
|We further define the coresilience of a number n > 1 as C(n)||=|
n − 1
|The coresilience of a prime p is C(p)||=|
Find the sum of all composite integers 1 < n ≤ 2×1011, for which C(n) is a unit fraction.