Divisor function: Difference between revisions

Revision as of 02:01, 10 March 2022

Revision as of 14:44, 21 March 2022

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Clearly, <math>1 < \sigma_0(n) < n</math> for all <math>n > 2</math>, and <math>\sigma_x(n) > n </math> for all <math>n > 1</math>, <math>x > 0</math> .

The divisor function is [[multiplicative function|multiplicative]],{{Why|date=May 2021|reason=the(since each divisor function''c'' of the product doesn't'mn'' seemwith obviously<math>\gcd(m, multiplicative.n) = What1</math> isdistinctively thecorrespond proofto sketch?}}a divisor ''a'' of ''m'' and a divisor ''b'' of ''n''), but not [[Completely multiplicative function|completely multiplicative]]:

:<math>\gcd(a, b)=1 \Longrightarrow \sigma_x(ab)=\sigma_x(a)\sigma_x(b).</math>