mathematical ternary operator: Dirichlet convolution (a×b)(c)

a,b are arithmetic functions, c is an integer (the output is defined for at least strictly positive integers c). (a×b)(c) is given by the sum (over all of the distinct ordered pairs (n,m) belonging to the Cartesian product of the set of all strictly positive integers with itself, such that n is not equal to m and such that nm = c (where adjacency represents typical multiplication of integers)) of a(n)b(m) (where adjacency represents typical pointwise multiplication).

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*(exp!)* - quaternary mathematical operator: (left) convolution (a★b)(c) in structure d