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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