Divisor function

Builds on Divisors of a natural number Arithmetic function

Definition

Let $k$ be a natural number. The divisor function $\sigma_k$ is the arithmetic function given by $\sigma_k(n) = \sum_{d \mid n} d^k,$ where the sum runs over the positive divisors $d$ of $n$ .

Remarks

The case $k = 0$ is the number of divisors, and the case $k = 1$ is the sum of divisors. For example, $\sigma_2(6) = 1 + 4 + 9 + 36 = 50$ . The same formula defines $\sigma_k$ for each real or complex number $k$ . The function $\sigma_k$ is multiplicative.

Reading path

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Arithmetic function definition
Divisibility definition
Divisors of a natural number definition
Divisor function definition

Where this leads

8 pages build on this one.

Tag	`0YEW47VJ0J`
URI	`m2://0YEW47VJ0J`
Kind	definition
Writing	W1 stated
MSC	11A25
Defines	Divisor function
Uses	Divisors of a natural number, Arithmetic function

Divisor function

Definition

Remarks

Reading path

Where this leads

Further reading

What this page needs for W2

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