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Victor Ufnarovski studied the arithmetic derivative with Bo Åhlander. Their definition assigns derivative one to every prime number and extends by the product rule. For $n=\prod p_i^{a_i}$, the resulting formula $n{\sum }_i{a}_i/p_i$ turns differentiation into an operation governed by integer factorization, rather than an ordinary derivative of a real-variable function.^[ref]