Divisors
✖
Divisors
Details and Options
- Divisors[n,GaussianIntegers->True] includes divisors that are Gaussian integers.
Examples
open allclose allBasic Examples (1)Summary of the most common use cases
Scope (2)Survey of the scope of standard use cases
For integer input, integer divisors are returned:
https://wolfram.com/xid/0c12yho-k0cy37
For Gaussian integer input, Gaussian divisors are produced:
https://wolfram.com/xid/0c12yho-fnl4s1
Divisors threads element‐wise over list arguments:
https://wolfram.com/xid/0c12yho-mf2sl8
Options (3)Common values & functionality for each option
GaussianIntegers (3)
This will produce Gaussian divisors for integer input:
https://wolfram.com/xid/0c12yho-bfsagk
Some primes are also Gaussian primes:
https://wolfram.com/xid/0c12yho-bw15y1
https://wolfram.com/xid/0c12yho-byf5mt
The ratio of Gaussian divisors to integer divisors:
https://wolfram.com/xid/0c12yho-jye2p
Applications (3)Sample problems that can be solved with this function
Find all perfect numbers less than 10000:
https://wolfram.com/xid/0c12yho-bpfovh
Representation of 25 as sum of two squares:
https://wolfram.com/xid/0c12yho-d18pln
PowersRepresentations generates an ordered representation:
https://wolfram.com/xid/0c12yho-3i45x7
Number of representations of a number as a sum of four squares:
https://wolfram.com/xid/0c12yho-exswgm
Computation by SquaresR:
https://wolfram.com/xid/0c12yho-bh0gvx
Properties & Relations (4)Properties of the function, and connections to other functions
This counts the number of divisors:
https://wolfram.com/xid/0c12yho-klc79o
https://wolfram.com/xid/0c12yho-jrwz8y
In general, DivisorSigma[d,n]==∑knkd:
https://wolfram.com/xid/0c12yho-urs5r
Similarly, EulerPhi[n]==n∏pn(1-1/p) where p is prime:
https://wolfram.com/xid/0c12yho-9nj6
https://wolfram.com/xid/0c12yho-cvqiq0
Alternatively, EulerPhi[n]==n∑knMoebiusMu[k]/k:
https://wolfram.com/xid/0c12yho-blx2dc
https://wolfram.com/xid/0c12yho-jcrs44
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:
https://wolfram.com/xid/0c12yho-e439h7
https://wolfram.com/xid/0c12yho-na9gp8
https://wolfram.com/xid/0c12yho-cr9eu8
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
]}
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
]}