csat-suneung 2020 Q17

csat-suneung · South-Korea · csat__math-humanities 4 marks Number Theory Arithmetic Functions and Multiplicative Number Theory

Let $f ( n )$ denote the number of positive divisors of a natural number $n$, and let $a _ { 1 } , a _ { 2 } , a _ { 3 } , \cdots , a _ { 9 }$ be all positive divisors of 36. What is the value of $\sum _ { k = 1 } ^ { 9 } \left\{ ( - 1 ) ^ { f \left( a _ { k } \right) } \times \log a _ { k } \right\}$? [4 points]
(1) $\log 2 + \log 3$
(2) $2 \log 2 + \log 3$
(3) $\log 2 + 2 \log 3$
(4) $2 \log 2 + 2 \log 3$
(5) $3 \log 2 + 2 \log 3$

Let $f ( n )$ denote the number of positive divisors of a natural number $n$, and let $a _ { 1 } , a _ { 2 } , a _ { 3 } , \cdots , a _ { 9 }$ be all positive divisors of 36.\\
What is the value of $\sum _ { k = 1 } ^ { 9 } \left\{ ( - 1 ) ^ { f \left( a _ { k } \right) } \times \log a _ { k } \right\}$? [4 points]\\
(1) $\log 2 + \log 3$\\
(2) $2 \log 2 + \log 3$\\
(3) $\log 2 + 2 \log 3$\\
(4) $2 \log 2 + 2 \log 3$\\
(5) $3 \log 2 + 2 \log 3$

Paper Questions

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