| The theory of numbers are an ancient mathematics branches and it mainly studies properties of the whole numbers. The first scientific approach to the study of integers, that is, the true origin of the theory of numbers,is generally attributed to the Greeks.Around 600 BC Pythagoras and his disciple made rather thorough studied of the integers. Up to now day, the theory of numbers has been already developed more mature and perfect, it also appear a lot of branches, such as, the elementary number theory, analytic number theory, algebra number theory etc., and The theory of numbers have a fairly good application to our society nowadays. For example: in the network communication and the calculation complexity and the cryptography.I studied the mean value of the square root sequence and arithmetical function U(n) and dual factorial part sequence, by studied, got the mean value and the Hybid mean value formula of them. The main achievements contained in this dissertation are as follows:Chapter f For convenience, this chapter give the topic study in this text of research background and meaning, explained the present condition of domestic and international research, then give some main research results to did cushion for the textual research.Chapter 2 This chapter discuss the mean value of the square root sequence, first, defined the square root sequence; second, to studied the functionφ(a2(n)), d(a2(n)) and theirs generation form of mean; third, discuss the mean value of the quare root sequence and the cube root sequence. Finally got their mean value formulas.Chapter 3 This chapter emphasize research the mean value of arithmetic function U(n) , is divided the function(?)and functionΦ(U(n)) and functionσα(U(n)) intoresearch. Finally got some interesting mean value calculation formula.Chapter 4 This chapter discuss the dual factorial part sequence.Firstly, introduce the dual factorial part sequence notion; secondly, studied the collect and divergence of the dual factorial part sequence. |
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