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NumberTheory

  

NumberOfPrimeFactors

  

number of prime factors counted with multiplicity

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

NumberOfPrimeFactors(n)

Omega(n)

Ωn

Parameters

n

-

integer

Description

• 

The NumberOfPrimeFactors(n) command computes the number of prime factors of the integer n counted with multiplicity.

• 

Every prime number divides 0 evenly, so 0 has infinitely many prime factors. However, for consistency with, for example, the Divisors command, NumberOfPrimeFactors(0) returns an error.

• 

To determine the number of distinct prime divisors of n (that is, without respect to multiplicity), use the distinct = true (or just distinct) option.

• 

Omega and Ω are aliases of NumberOfPrimeFactors.

• 

You can enter the command Omega using either the 1-D or 2-D calling sequence. For example, Omega(8) is equivalent to Ω8.

Examples

withNumberTheory:

NumberOfPrimeFactors5

1

(1)

NumberOfPrimeFactors9

2

(2)

NumberOfPrimeFactors12

3

(3)

NumberOfPrimeFactors12,'distinct'

2

(4)

Ω57

2

(5)

Si=1nΩfi

Si=1nΩfi

(6)

evalS,f=k→2k+1,n=15

21

(7)

NumberOfPrimeFactors0

Error, (in NumberTheory:-NumberOfPrimeFactors) 0 has infinitely many prime factors

Compatibility

• 

The NumberTheory[NumberOfPrimeFactors] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

NumberTheory

NumberTheory[PrimeFactors]