On the normal number of prime factors of \(\phi(n)\) (Q1821814)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the normal number of prime factors of \(\phi(n)\) |
scientific article; zbMATH DE number 4000050
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the normal number of prime factors of \(\phi(n)\) |
scientific article; zbMATH DE number 4000050 |
Statements
On the normal number of prime factors of \(\phi(n)\) (English)
0 references
1985
0 references
The authors prove that the number of prime factors (either distinct or counted with multiplicities) of Euler's function \(\phi(n)\) obeys the Gaussian distribution law. The normal order equals \((\log\log n)^3/2\) and the standard deviation is \(3^{-1/2}(\log\log n)^{3/2}\).
0 references
Euler phi-function
0 references
number of prime factors
0 references
normal order
0 references
standard deviation
0 references
