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2009-04-29T02:05:52Z

Created page with '{{arithmetic function}} ==Definition== Let <math>n</math> be a natural number. The '''prime divisor count function''' of <math>n</math>, denoted <math>\omega(n)</math>, is ...'

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{{arithmetic function}}

==Definition==

Let <math>n</math> be a [[natural number]]. The '''prime divisor count function''' of <math>n</math>, denoted <math>\omega(n)</math>, is defined as the number of prime divisors of <math>n</math>.

==Relation with other arithmetic functions==

* [[Mobius function]]: This is defined as <math>(-1)^{\omega(n)}</math> for <math>n</math> a [[square-free number]], and is <math>0</math> otherwise.
* [[Divisor count function]]: This is denoted <math>\tau(n)</math>, and is defined as the total number of positive divisors of <math>n</math>.
* [[Largest prime power divisor]]: Denoted <math>q(n)</math>, this is defined as the largest prime power dividing <math>n</math>. We have:

<math>\omega(n)\log(q(n)) \ge \log(n)</math>.

Prime divisor count function - Revision history

Vipul: Created page with '{{arithmetic function}} ==Definition== Let n be a natural number. The '''prime divisor count function''' of n, denoted \omega(n), is ...'

Vipul: Created page with '{{arithmetic function}} ==Definition== Let $n$ be a natural number. The '''prime divisor count function''' of $n$ , denoted $\omega(n)$ , is ...'