# The answer is very common.

Number Theory Level pending

Compute upto 3 decimal places:

$\large{\prod _{ k=1 }^{ \infty }{ { \left( 1-\frac { 1 }{ \phi ^{ k } } \right) }^{ \frac { \mu \left( k \right) -\varphi \left( k \right) }{ k } } } }$

Details and Assumption

• $$\mu \left( k \right)$$ is mobius function
• $$\varphi \left( k \right)$$ is Euler's totient function.
• $$\phi =\frac { 1+\sqrt { 5 } }{ 2 }$$
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