Divisor function: Difference between revisions

Revision as of 18:18, 30 May 2021

Revision as of 18:27, 30 May 2021

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since ''n'' prime factors allow a sequence of binary selection (<math>p_{i}</math> or 1) from ''n'' terms for each proper divisor formed.

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

The divisor function is [[multiplicative function|multiplicative]],{{Why|date=May 2021|reason=the divisor function doesn't seem obviously multiplicative. What is the proof sketch?}} but not [[Completely multiplicative function|completely multiplicative]]: