A unitary divisor is a positive divisor 
of a positive integer 
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 positive
integer 
can be computed in the Wolfram Language
using:
UnitaryDivisors[1] = {1};
UnitaryDivisors[n_Integer] /; n > 1 := Sort[Flatten[Outer[
Times, Sequence @@ ({1, #}& /@
Power @@@ FactorInteger[n])
]]]
The following table gives the unitary divisors for the first few positive 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)
|
where the 
are distinct primes and the 
are positive integers,
 |
(3)
|
is a unitary divisor of 
iff each 
is 0 or 
. For a prime power 
, the unitary divisors are 1 and 
, where 
is a positive integer
(Cohen 1990).
The symbol 
is used to denote 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 distinct primes
dividing 
.
