An Inequality for the Arithmetical Function g(x)

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Authors

  • Muslim University, Aligarh ,IN

DOI:

https://doi.org/10.18311/jims/1939/17291

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.