Definition: Sum of Divisors

The sum of divisors function $F:\mathbb N\to\mathbb N$ is an arithmetic function, which maps a given number $n\in\mathbb N,$ $n > 0$ to the sum of its divisors. In the sum notation, the $F$ function can be written as $$F(n):=\sum_{d \mid n}d\quad\quad\forall n > 0.$$

Example.

The $F$ function can be visualized using SageMath. If you click on the evaluate button, you will see the values of $F(n)$ for $n=1,\ldots,100.$

sigmapoints= [(i, sigma(i,1)) for i in range(1,100)] list_plot(sigmapoints)

Definitions: 1
Proofs: 2
Propositions: 3


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References

Bibliography

  1. Landau, Edmund: "Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927