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1000∑n=0∞σ0(6n)6n1000\sum _{ n=0 }^{ \infty }{ \frac { { \sigma }_{ 0 }\left( { 6 }^{ n } \right) }{ { 6 }^{ n } } } 1000n=0∑∞6nσ0(6n)
Find the value of the expression above if σ0(x){ \sigma }_{ 0 }\left( x \right) σ0(x) is the number of factors of xxx. 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 σ0(4)=3.
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