Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1993. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 21)

James P. Jones and Péter Kiss: Properties of The Least Common Multiple Function

JAMES P. JONES and PÉTER KISS PROPERTIES OF THE LEAST COMMON MULTIPLE FUNCTION* ABSTRACT: In this paper we show some properties of the function L(x), the least common multiple of the natural numbers not greater than an integer x, and the function Q(x) = x\/L(x). The subject of this paper is to show the number-theoretic properties of the function L(x) = LCM[\,2,...,x], the least common multiple of the numbers < x. This function has a connection with the function FI(x)

, the number of primes < x and it is related to the two Chebyshev functions y/(x) = ln(l(x)) and 6{x) for which 0(x)= 2>0) and y/(x) = 0(x) + 6(x

]/

2) + 0(x

V

3)+... p< X ' Research was supported by the Hungarian National Foundation (Grant No. 1641) for Scientific Research and the National Scienfitic and Engineering Reseurch Council of Canada. 65