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
, representing the unitary sigma function and unitary phi
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
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