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numtheory

  

sigma

  

sum of divisors

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

sigma(n)

sigma[k](n)

Parameters

k

-

integer

n

-

integer

Description

• 

Important: The numtheory[sigma] command has been deprecated.  Use the superseding command NumberTheory[SumOfDivisors] instead.

• 

The function sigma(n) will compute the sum of the positive divisors of n.

• 

The function sigma[k](n)  will compute the sum of the kth power of positive divisors of n.

• 

This function is part of the numtheory package, and so can be used in the form sigma[..](..) only after performing the command with(numtheory) or with(numtheory, sigma).  The function sigma(..) can always be accessed in the above form or the long form numtheory[sigma](..).

Examples

withnumtheory:

σ9

13

(1)

divisors100

1,2,4,5,10,20,25,50,100

(2)

σ100

217

(3)

σ[0]100

9

(4)

τ100

9

(5)

See Also

ifactor

ifactors

numtheory[divisors]

numtheory[factorset]

numtheory[tau]

 


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