The Journal of the Indian Mathematical Society

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An Inequality for the Arithmetical Function g(x)


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1 Muslim University, Aligarh, India
     

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Let n = a1 + a2 + .......... + ap, and f(n) the maximum of the least common multiple of a1, a2, .. ., ap for all such positive a's. Landau has proved that if log f(x)=g(x), then

lim g(x)/(x logx)1/2 = 1.                                         (1)

Let p denote a prime number.


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  • An Inequality for the Arithmetical Function g(x)

Abstract Views: 247  |  PDF Views: 0

Authors

S. M. Shah
Muslim University, Aligarh, India

Abstract


Let n = a1 + a2 + .......... + ap, and f(n) the maximum of the least common multiple of a1, a2, .. ., ap for all such positive a's. Landau has proved that if log f(x)=g(x), then

lim g(x)/(x logx)1/2 = 1.                                         (1)

Let p denote a prime number.