number of distinct prime factors function
The number of distinct prime factors function counts how many distinct prime factors has. Expressing as
where the are distinct primes, there being of them, and the are positive integers (not necessarily distinct), then .
Obviously for a prime it follows that . When is a squarefree number, then , where is the number of (nondistinct) prime factors function (http://planetmath.org/NumberOfNondistinctPrimeFactorsFunction). Otherwise, .
is an additive function, and it can be used to define a multiplicative function like the Möbius function (as long as is squarefree).
Title | number of distinct prime factors function |
---|---|
Canonical name | NumberOfDistinctPrimeFactorsFunction |
Date of creation | 2013-03-22 16:06:52 |
Last modified on | 2013-03-22 16:06:52 |
Owner | CompositeFan (12809) |
Last modified by | CompositeFan (12809) |
Numerical id | 9 |
Author | CompositeFan (12809) |
Entry type | Definition |
Classification | msc 11A25 |
Related topic | NumberOfNondistinctPrimeFactorsFunction |
Related topic | 2omeganLeTaunLe2Omegan |