We prove an Ω result on the average of the sum of the divisors of n which are relatively coprime to any given integer a. This generalizes the earlier result for a prime proved by Adhikari, Coppola and Mukhopadhyay.
Let , be two independent, -dimensional bifractional Brownian motions with respective indices and . Assume . One of the main motivations of this paper is to investigate smoothness of the collision local time where denotes the Dirac delta function. By an elementary method we show that is smooth in the sense of Meyer-Watanabe if and only if .
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