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On the Number of Certain Relatively Prime Subsets of {1, 2, . . . , n}
Published/Copyright:
September 9, 2010
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
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- Two New Van Der Waerden Numbers: w(2; 3, 17) and w(2; 3, 18)
- Distance Graphs from p-adic Norms
- A Note on Stirling Series
- On the Number of Certain Relatively Prime Subsets of {1, 2, . . . , n}
- Powers of Sierpiński Numbers Base b
- Subsets of ℤ with Simultaneous Orderings
- Alternative Proofs on the 2-adic Order of Stirling Numbers of the Second Kind
- On Relatively Prime Sets Counting Functions
- Congruences for Overpartition k-tuples
Keywords for this article
Relatively prime integers;
Euler's function;
gcd-sum function;
binomial coefficient;
integer composition;
integer partition;
formal series;
asymptotic formula
Articles in the same Issue
- Two New Van Der Waerden Numbers: w(2; 3, 17) and w(2; 3, 18)
- Distance Graphs from p-adic Norms
- A Note on Stirling Series
- On the Number of Certain Relatively Prime Subsets of {1, 2, . . . , n}
- Powers of Sierpiński Numbers Base b
- Subsets of ℤ with Simultaneous Orderings
- Alternative Proofs on the 2-adic Order of Stirling Numbers of the Second Kind
- On Relatively Prime Sets Counting Functions
- Congruences for Overpartition k-tuples
