One of three of a kind - Part (3) - Final

n=1(11ϕn)[μ(n)φ(n)]/n\Large \prod_{n=1}^{\infty} \left(1-\frac{1}{\phi^n}\right)^{[\mu(n)-\varphi(n)]/n}

What is the value of the product above?

Note: φ\varphi is the Euler totient function, μ\mu is the Moebius function, and ϕ=1+52\phi = \dfrac{1+\sqrt5}{2} is the golden ratio.


Part 1 and Part 2.

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