WOLFRAM

gives a list of the integers that divide n.

Details and Options

Examples

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Basic Examples  (1)Summary of the most common use cases

The divisors of 1729:

Out[1]=1
Out[2]=2

Scope  (2)Survey of the scope of standard use cases

For integer input, integer divisors are returned:

Out[1]=1

For Gaussian integer input, Gaussian divisors are produced:

Out[2]=2

Divisors threads elementwise over list arguments:

Out[1]=1

Options  (3)Common values & functionality for each option

GaussianIntegers  (3)

This will produce Gaussian divisors for integer input:

Out[1]=1

Some primes are also Gaussian primes:

Out[1]=1
Out[2]=2

The ratio of Gaussian divisors to integer divisors:

Out[1]=1

Applications  (3)Sample problems that can be solved with this function

Find all perfect numbers less than 10000:

Out[1]=1

Representation of 25 as sum of two squares:

Out[1]=1

PowersRepresentations generates an ordered representation:

Out[2]=2

Number of representations of a number as a sum of four squares:

Out[1]=1

Computation by SquaresR:

Out[2]=2

Properties & Relations  (4)Properties of the function, and connections to other functions

This counts the number of divisors:

Out[1]=1
Out[2]=2

In general, DivisorSigma[d,n]==k|nkd:

Out[1]=1

Similarly, EulerPhi[n]==np|n(1-1/p) where p is prime:

Out[1]=1
Out[2]=2

Alternatively, EulerPhi[n]==nk|nMoebiusMu[k]/k:

Out[1]=1
Out[2]=2

Possible Issues  (1)Common pitfalls and unexpected behavior

Divisors gives all divisors except for multiplication by units; that is, they lie in the first quadrant:

Out[1]=1

Get all divisors:

Out[2]=2
Out[3]=3
Wolfram Research (1988), Divisors, Wolfram Language function, https://reference.wolfram.com/language/ref/Divisors.html.
Wolfram Research (1988), Divisors, Wolfram Language function, https://reference.wolfram.com/language/ref/Divisors.html.

Text

Wolfram Research (1988), Divisors, Wolfram Language function, https://reference.wolfram.com/language/ref/Divisors.html.

Wolfram Research (1988), Divisors, Wolfram Language function, https://reference.wolfram.com/language/ref/Divisors.html.

CMS

Wolfram Language. 1988. "Divisors." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Divisors.html.

Wolfram Language. 1988. "Divisors." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Divisors.html.

APA

Wolfram Language. (1988). Divisors. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Divisors.html

Wolfram Language. (1988). Divisors. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Divisors.html

BibTeX

@misc{reference.wolfram_2024_divisors, author="Wolfram Research", title="{Divisors}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Divisors.html}", note=[Accessed: 09-January-2025 ]}

@misc{reference.wolfram_2024_divisors, author="Wolfram Research", title="{Divisors}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Divisors.html}", note=[Accessed: 09-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_divisors, organization={Wolfram Research}, title={Divisors}, year={1988}, url={https://reference.wolfram.com/language/ref/Divisors.html}, note=[Accessed: 09-January-2025 ]}

@online{reference.wolfram_2024_divisors, organization={Wolfram Research}, title={Divisors}, year={1988}, url={https://reference.wolfram.com/language/ref/Divisors.html}, note=[Accessed: 09-January-2025 ]}