Publication date
January 2001
DOI Publisher
Academic Press. ISSN
0022-314X Citation count (estimate)
20Abstract
RésuméLet 1=d1(n)<d2(n)<…<dτ(n)=n be the sequence of all the divisors of the integer n in increasing order. Let us say that the divisors of n are y-dense iff max1⩽i<τ(n)di+1(n)/di(n)⩽y, and let D(x, y, z) be the number of positive integers less than x whose divisors are y-dense and whose prime divisors are bigger than z. We show the existence of three positive constants c1, c2, and y0 such that c1⩽(logx·logz)D(x, y, z)/xlog(y/z)⩽c2 for all x, y, and z in the region x⩾y⩾z+z0.535⩾3, x⩾z5, and y⩾y0. We give also a general upper bound for D(x, y, z) without any condition on x, y, and z
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