Average Values of Mean Squares in Factorials
نویسندگان
چکیده
منابع مشابه
On values of arithmetical functions at factorials I
has d(k!) d((k I)!) solutions, where d(n) denotes the number of divisors of n. This follows from {x: S(x) = k} = {x: xlk!, x t (k I)!}. Thus, equation (1) always has at least a solution, if d(k!) > d((k I)!) for k ~ 2. In what follows, we shall prove this inequality, and in fact we will consider the arithmetical functions y, <7, d, w, 0 at factorials. Here y( n) = Euler's arithmetical function,...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1956
ISSN: 0003-4851
DOI: 10.1214/aoms/1177728067