Let denote the number of positive divisors of the positive integer , and the sum of the positive divisors of . Show that

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- May 18th 2010, 01:49 PMBruno J.[SOLVED] Sum of divisors
Let denote the number of positive divisors of the positive integer , and the sum of the positive divisors of . Show that

- May 18th 2010, 04:46 PMNonCommAlg
- May 18th 2010, 04:57 PMBruno J.
Great job! (Thanks for specifying (Giggle)).

Here's how I proved the first inequality; we have , and by the arithmetic/geometric mean inequality. - May 18th 2010, 05:03 PMNonCommAlg