to certain modified unitary Ramanujan sums, 213-223

We introduce new analogues of the Ramanujan sums, denoted by
, associated with unitary divisors, and
obtain results concerning the expansions of arithmetic functions of several variables with respect to the sums
. We apply
these results to certain functions associated with
and , representing the unitary sigma function and unitary phi
function, respectively.

Key Words: Ramanujan expansion of arithmetic functions, arithmetic function of several variables, multiplicative function, unitary divisor, sum of unitary divisors, unitary Euler function, unitary Ramanujan sum.

2010 Mathematics Subject Classification: Primary 11A25. Secondary 11N37