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Abstract
We give common generalizations of three formulae involving the number of relatively prime subsets of {1, 2, . . . , n} with some additional constraints. We also generalize a fourth formula concerning the Euler-type function Φk, and investigate certain related divisor-type, sum-of-divisors-type and gcd-sum-type functions.
Keywords.: Relatively prime integers; Euler's function; gcd-sum function; binomial coefficient; integer composition; integer partition; formal series; asymptotic formula
Received: 2009-10-21
Revised: 2010-04-09
Accepted: 2010-04-11
Published Online: 2010-09-09
Published in Print: 2010-September
© de Gruyter 2010
