Geodesic
Relatively prime sets and a phi function for subsets of $\{1, 2,\dots, n\}$
Journal of integer sequences, Tome 13 (2010) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     title = {Relatively prime sets and a phi function for subsets of $\{1, 2,\dots, n\}$},
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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/