---
tag: 0RXKW044R4
kind: concept
name: Completely multiplicative function
msc: [11A25]
sources:
  - url: https://en.wikipedia.org/wiki/Completely_multiplicative_function
    locator: lead section
same_as:
  wikidata: Q5156533
  wikipedia: Completely multiplicative function
---

## Summary

A completely multiplicative function is an arithmetic function with $f(1) = 1$ and $f(mn) = f(m) f(n)$ for all positive integers $m$ and $n$.
The [[definition of a completely multiplicative function|0GS27TKF1V]] gives the precise form.