The sum-of-unitary-divisors function is denoted by the lowercase Greek letter sigma thus: σ*(n).
The sum of the k-th powers of the unitary divisors is denoted by σ*k(n): It is a multiplicative function.
The sum of the unitary divisors of n is odd if n is a power of 2 (including 1), and even otherwise.
The Dirichlet generating function is Every divisor of n is unitary if and only if n is square-free.
Equivalently, the set of unitary divisors of n forms a Boolean ring, where the addition and multiplication are given by where
[The number of bi-unitary divisors of an integer, in The Theory of Arithmetic Functions, Lecture Notes in Mathematics 251: 273–282, New York, Springer–Verlag].
The number of bi-unitary divisors of n is a multiplicative function of n with average order