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Definition: Given two series sum(a_n) and sum(b_n), with a_0 = b_0 = 0. Define c_n = sum_(d/n)[(a_d)(b_n/d)] for all n, where sum_n/d means a sum extended over all positive divisors of n (including 1 and n). For example, c_6 = (a_1)(b_6) + (a_2)(b_3) + (a_3)(b_2) + (a_6)(b_1), and c_7 = (a_1)(b_7) + (a_7)(b_1). We call c_n a Dirichlet product.
Source: Mathematical Analysis, second edition by Tom M. Apostol