On the integer part of the M - th root and the largest M - th power not exceeding
نویسندگان
چکیده
Let m be a fixed positive integer. For any positive integer n, we define the arithmetical function am(n) as the integer part of the m-th root of n. That is, am(n) = [n 1 m ], where [x] denotes the greatest integer not exceeding to x. For example, a2(1) = 1, a2(2) = 1, a2(3) = 1, a2(4) = 2, a2(5) = 2, a2(6) = 2, a2(7) = 2, a2(8) = 2, a2(9) = 3, a2(10) = 3, · · · . In [1], Professor F. Smarandache asked us to study the properties of the sequences {ak(n)}. About this problem, Z. H. Li [2] studied its mean value properties, and given an interesting asymptotic formula: ∑
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