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Soient λ > 1 , 0 < η < 1 2 et g ( n ) une fonction multiplicative vérifiant g ( p ) = 1 / λ g ( n ) n - η . Dans ce travail, on établit une formule asymptotique de la somme n g ( n ) x ; P ( n ) y 1 , valable dans le domaine exp ( log log c x ) 5 3 + ϵ y / λ c x , et on donne une condition nécessaire et suffisante pour que cette somme soit équivalente à n x ; P ( n ) y 1 / g ( n ) .