A divisor 
of 
for which
 |
(1)
|
where 
is the greatest common divisor. For example,
the divisors of 12 are 
,
so the unitary divisors are 
. A list of unitary divisors of a number 
an be computed in the Wolfram
Language using:
UnitaryDivisors[n_Integer] := Sort[Flatten[Outer[
Times, Sequence @@ ({1, #}& /@
Power @@@ FactorInteger[n])
]]]
The following table gives the unitary divisors for the first few integers (OEIS A077610).
 |  |
| 1 | 1 |
| 2 | 1, 2 |
| 3 | 1, 3 |
| 4 | 1, 4 |
| 5 | 1, 5 |
| 6 | 1, 2, 3, 6 |
| 7 | 1, 7 |
| 8 | 1, 8 |
| 9 | 1, 9 |
| 10 | 1, 2, 5, 10 |
| 11 | 1, 11 |
| 12 | 1, 3, 4, 12 |
| 13 | 1, 13 |
| 14 | 1, 2, 7, 14 |
| 15 | 1, 3, 5, 15 |
Given the prime factorization
 |
(2)
|
then
 |
(3)
|
is a unitary divisor of 
if each 
is 0 or 
.
For a prime power 
, the unitary divisors are 1 and 
(Cohen 1990).
The symbol 
is used to denote to the unitary divisor function.
The numbers of unitary divisors 
of 
, 2, ... are 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4,
2, 2, 4, 2, 4, ... (OEIS A034444). These numbers
are also the numbers of squarefree divisors of 
. The number of unitary divisors of 
is also given by 
, where 
is the number of different primes dividing 
.
