# Menon-type identities concerning subsets of the set $\{1,2,\ldots,n\}$

@inproceedings{Toth2021MenontypeIC, title={Menon-type identities concerning subsets of the set \$\\{1,2,\ldots,n\\}\$}, author={L'aszl'o T'oth}, year={2021} }

d|n 1 is the divisor function. Identity (1.1) is due to P. K. Menon [6], and it has been generalized in various directions by several authors, also in quite recent papers. See, e.g., [1, 2, 3, 4, 5, 10, 11, 12, 13] and their references. For a nonempty subset A of {1, 2, . . . , n} let (A) denote the gcd of the elements of A. Then A is said to be relatively prime if (A) = 1, i.e., the elements of A are relatively prime. Let f(n) denote the number of relatively prime subsets of {1, 2, . . . , n… Expand

#### One Citation

Proofs, generalizations and analogs of Menon's identity: a survey

- Mathematics
- 2021

Menon’s identity states that for every positive integer n one has ∑ (a− 1, n) = φ(n)τ(n), where a runs through a reduced residue system (mod n), (a − 1, n) stands for the greatest common divisor of a… Expand

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