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 \({ \sigma }_{ 0 }\left( 4 \right)=3 \).
by
Joel Yip