## tribble.math.misc Class PrimeFactors

java.lang.Object
tribble.math.misc.PrimeFactors

public class PrimeFactors
extends java.lang.Object

Determine the number of prime factors for a sequence of naturals.

Utilizes a function (rediscovered by the author, Sep 2006) which determines the number of prime factors for a given natural (integer). The function omega() is defined as:
Omega(0) = 0
;
Omega(1) = 0
;
Omega(p) = 1, for any prime p;
Omega(pk) = Omega(k)+1, for any prime p.

See sequence A001222 at the On-Line Encyclopedia of Integer Sequences.

Since:
2006-09-10
Version:
\$Revision: 1.2 \$ \$Date: 2006/09/10 15:28:35 \$
Author:
David R. Tribble (david@tribble.com)

Constructor Summary
PrimeFactors()

Method Summary
static void main(java.lang.String[] args)

static int omega(int n)
Determine the number of prime factors for a given natural.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

### PrimeFactors

public PrimeFactors()
Method Detail

### omega

public static int omega(int n)
Determine the number of prime factors for a given natural.

This function is defined as:
Omega(0) = 0
;
Omega(1) = 0
;
Omega(p) = 1, for any prime p;
Omega(pk) = Omega(k)+1, for any prime p.

Parameters:
n - A natural.
Since:
2006-09-09

### main

public static void main(java.lang.String[] args)