This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Divisors

 Divisors[n]gives a list of the integers that divide n.
The divisors of 1729:
The divisors of 1729:
 Out[1]=
 Out[2]=
 Scope   (2)
For integer input, integer divisors are returned:
For Gaussian integer input, Gaussian divisors are produced:
Divisors threads element-wise over list arguments:
 Options   (3)
This will produce Gaussian divisors for integer input:
Some primes are also Gaussian primes:
The ratio of Gaussian divisors to integer divisors:
 Applications   (3)
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:
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