Dirichlet convolution is a mathematical operation used primarily in number theory, particularly in the study of arithmetic functions. Given two arithmetic functions f and g , their Dirichlet convolution, denoted as f * g , is defined for any positive integer n as the sum of the products of the values of f and g at divisors of n . Mathematically, it is expressed as (f * g)(n) = \sum_d|n f(d)g(n/d) . This operation is significant because it allows for the construction of new arithmetic functions from existing ones. For example, the Möbius function and the Euler's totient function can be combined using Dirichlet convolution to derive properties of integers. Dirichlet convolution is also essential in the study of multiplicative functions, which are functions where the value at a product of cop