This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Divisors

Divisors[n]
gives a list of the integers that divide n.
The divisors of 1729:
The divisors of 1729:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
For integer input, integer divisors are returned:
For Gaussian integer input, Gaussian divisors are produced:
Divisors threads element-wise over list arguments:
This will produce Gaussian divisors for integer input:
Some primes are also Gaussian primes:
The ratio of Gaussian divisors to integer divisors:
Find all less than 10000:
Representation of 25 as sum of two squares:
PowersRepresentations generates an ordered representation:
Number of representations of a number as a sum of four squares:
Computation by SquaresR:
This counts the number of divisors:
In general, DivisorSigma[d, n]==k|nkd:
Similarly, EulerPhi[n]==np|n(1-1/p) where p is prime:
Alternatively, EulerPhi[n]==nk|nMoebiusMu[k]/k:
Divisors gives all divisors except for multiplication by units, that is, they lie in the first quadrant:
Get all divisors:
New in 1