Number of factors is too easy

Number Theory Level 4

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

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

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

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