Average order of the cardinality of some sets of prime factors (Q1335539)
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: Average order of the cardinality of some sets of prime factors |
scientific article; zbMATH DE number 650852
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Average order of the cardinality of some sets of prime factors |
scientific article; zbMATH DE number 650852 |
Statements
Average order of the cardinality of some sets of prime factors (English)
0 references
9 October 1994
0 references
Die bekannte asymptotische Entwicklung der Primteilerfunktion \[ \sum_{n\leq x} \omega(n)= x\log\log x+Ax+ O\biggl( {x\over {\log x}}\biggr) \] wird auf andere additive Funktionen \(f\) ausgedehnt, z.B. auf \(f(p^ \alpha)= \begin{cases} 1,\;&\alpha\geq k\\ 0, &\alpha< k\end{cases}\), also die Anzahlfunktion der \(k\)-vollen Teiler. Analoges wird für \(k\)-freie, \(k\)-vollständige, \(k\)-unitäre und ähnliche Teiler bewiesen. Die Beweise sind elementar und Varianten der bekannten.
0 references
arithmetical functions
0 references
asymptotic results on primes
0 references
number of \(k\)-full divisors
0 references
\(k\)-free divisors
0 references
\(k\)-complete divisors
0 references
\(k\)-unitary divisors
0 references
