What is the significance of g(x) in number theory?

zetafunction
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given the formula

g(x)= \sum_{n \le x}[ \frac{x}{n}]

has any meaning in number theory ? ,
 
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zetafunction said:
given the formula

g(x)= \sum_{n \le x}[ \frac{x}{n}]

has any meaning in number theory ? ,

See http://www.research.att.com/~njas/sequences/A006218 . This site should probably be your first choice to find information on any number sequence.
 
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