On the random variable {1,2,…,n}r∋(k1,k2,…,kr)↦gcd(n,k1k2⋯kr)∈N{1,2,…,n}r∋(k1,k2,…,kr)↦gcd(n,k1k2⋯kr)∈N

We compute the “moments” and its continuous analogue of the random variable Nr∋(k1,k2,…,kr)↦gcd(n,k1k2⋯kr)∈NNr∋(k1,k2,…,kr)↦gcd(n,k1k2⋯kr)∈N by an elementary method. This generalizes a result of Kurokawa–Ochiai, which computed its “average” using some analysis involving L-function.