Geodesic
Relatively prime sets and a Phi function for subsets of \(\{1, 2,\dots, n\}\)
Journal of integer sequences, Tome 13 (2010) no. 7
A nonempty subset $A$ of ${1, 2, \dots , n}$ is said to be relatively prime if $gcd(A) = 1$. Let $f(n)$ and $f_{k}(n)$ denote the number of relatively prime subsets and the number of relatively prime subsets of cardinality $k$ of ${1, 2, \dots , n}$, respectively. Let $\Phi (n)$ and $\Phi _{k}(n)$ denote the number of nonempty subsets and the number of subsets of cardinality $k$ of ${1, 2, \dots , n}$ such that $gcd(A)$ is relatively prime to $n$, respectively. In this paper, we obtain some properties of these functions.
Classification : 11A25, 11B75
Keywords: relatively prime subset, Euler phi function 
@article{JIS_2010__13_7_a3,
     author = {Tang,  Min},
     title = {Relatively prime sets and a {Phi} function for subsets of \(\{1, 2,\dots, n\}\)},
     journal = {Journal of integer sequences},
     year = {2010},
     volume = {13},
     number = {7},
     zbl = {1235.11010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_7_a3/}
}
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Tang,  Min. Relatively prime sets and a Phi function for subsets of \(\{1, 2,\dots, n\}\). Journal of integer sequences, Tome 13 (2010) no. 7. http://geodesic.mathdoc.fr/item/JIS_2010__13_7_a3/