An identity involving the function ep(n)
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چکیده
Let p be any fixed prime, n be any positive integer, ep(n) denotes the largest exponent of power p in n. That is, ep(n) = m, if p | n and p n. In problem 68 of [1], Professor F.Smarandache asked us to study the properties of the sequence {ep(n)}. About the elementary properties of this function, many scholars have studied it (see reference [2]-[7]), and got some useful results. For examples, Liu Yanni [2] studied the mean value properties of ep(bk(n)), where bk(n) denotes the k-th free part of n, and obtained an interesting mean value formula for it. That is, let p be a prime, k be any fixed positive integer, then for any real number x ≥ 1, we have the asymptotic formula ∑
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تاریخ انتشار 2013