Only a third are coprime?

Let x 1 , x 2 , x 3 , x_1, x_2, x_3, \ldots be all the distinct positive integers satisfying ϕ ( x ) = x 3 \phi(x) = \dfrac x3 .

Compute 1 x 1 + 1 x 2 + 1 x 3 + \dfrac1{x_1} + \dfrac1{x_2} + \dfrac1{x_3} + \cdots .


Notation: ϕ ( ) \phi(\cdot) denotes the Euler's totient function .


The answer is 0.5.

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