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A new arithmetical function and its mean value
Author(s): 
Pages: 351-354
Year: Issue:  3
Journal: PURE AND APPLIED MATHEMATICS

Keyword:  算术函数均值公式恒等式;
Abstract: 对任意正整数n,我们定义算术函数(Ω)(n)为(Ω)(1)=0,当n>1,且n=pα11·pα22…pαkk为n的标准分解式时,定义(Ω)(n)=α1p1+α2p2+…+αkpk.显然这个函数是可加函数.即就是对任意正整数m及n有(Ω)(m·n)=(Ω)(m)+(Ω)(n).本文主要目的是利用初等方法研究函数(Ω)(n)的算术性质,并给出一个较强的均值公式及有趣的恒等式.
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