For a positive integer m , let (m) denote the sum of positive divisors of m and (m) denote the number of elements of the set j: 1 j m with gcd (j, m)=1 , and define f(m)= (m) (m) . Let p, q be distinct primes and r, s be positive integers.

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For a positive integer m , let (m) denote the sum of positive divisors of m and (m) denote the number of elements of the set j: 1 j m with gcd (j, m)=1 , and define f(m)= (m) (m) . Let p, q be distinct primes and r, s be positive integers. Then

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Correct answer: D. f (p^r q^s )=f (p^r ) f (q^s )

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For a positive integer m , let (m) denote the sum of positive divisors of m and (m) denote the number of elements of the set j: 1 j m with gcd (j, m)=1 , and define f(m)= (m) (m) . Let p, q be distinct primes and r, s be positive integers. Then

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