Given n 2 1 , let os ( n) denote the sum of the sth powers of the positive divisors of n ; that is , Of ( n ) = gt; as d / n Verify the...

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Given n 2 1 , let os ( n) denote the sum of the sth powers of the positive divisors of n ; that is ,"Of ( n ) = > asd / nVerify the following :( 2 ) 00 = Tand 01 = 0.( 6) os is a multiplicative function .[ Hint : The function f, defined by An ) = ns , is multiplicative . ]( C) If 1 = PI P 2")The ... proOr is the prime factorization of n , thenOf ( 12 ) =~ 5 ( ^` + 1 ) _ ]PIP 2s ( kit! ) _ ]pstar + 1 ) _ 1}Pi - 1P2 - 1)PS - 1