Number of factors is too easy

1000n=0σ0(6n)6n1000\sum _{ n=0 }^{ \infty }{ \frac { { \sigma }_{ 0 }\left( { 6 }^{ n } \right) }{ { 6 }^{ n } } }

Find the value of the expression above if σ0(x){ \sigma }_{ 0 }\left( x \right) is the number of factors of xx. It is also called the divisor function.

As an explicit example, 4 has 3 factors 1,2 and 4, so σ0(4)=3{ \sigma }_{ 0 }\left( 4 \right)=3 .

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