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Let M be a subset of a given non-negative integer , SM = {n | n = p1α1 p2α2 ... pkαk \n), when n only in the SM value , study the mean value of f (n) is an interesting topic in the number theory . Vocabulary ω (n) is the number of distinct prime factors of n , T (n) is the divisor function, σ ( n ) , φ (n ) , respectively, for the divisor and functions, and the Euler function . this paper we for m = { 0,1, B1 , B2 , ... ) ( namely contains 0,1 non - negative integers subset) , and f (n) , respectively, the constant functions 1,2 Ω (n ) , T (n ) , σ ( n ) , φ (n ) and ( R GT ; 0 is an arbitrary real number ) of the case, to obtain the asymptotic formula .
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