SOLUTION: prove that for all positive integers n, sigma(2n) is greater than 2*sigma (n) (where sigma(n) denotes the sum of the divisors of n)

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: prove that for all positive integers n, sigma(2n) is greater than 2*sigma (n) (where sigma(n) denotes the sum of the divisors of n)      Log On


   

Question 841796: prove that for all positive integers n, sigma(2n) is greater than 2*sigma (n) (where sigma(n) denotes the sum of the divisors of n)
Answer by richard1234(7193) About Me  (Show Source):
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Let where is not divisible by 2. Since for relatively prime a,b we have





Also we have



And hence since .