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We study the mean value of generalized divisor functionsτ    κ    (  n  )over integers without large prime factors (hereκ  &gt;  0). We relate this problem to the computation of the ratioΨ    (    x    1   /   κ    ,  y  )    κ/   Ψ  (  x  ,  y  ), involving they-smooth numbers counting function. We establish an inverse theorem, giving limitations on the range in(  x  ,  y  )in which this ratio can be asymptotically estimated uniformly inκ.

Remarques sur les moyennes des fonctions de Piltz sur les entiers friables