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Let K(x, y) be the number in the title. There is a function/(/•), concave and decreasing with /(0) = 2 and /'(0) = 0 such that if r = ^Aog x /log y then as x -» oo with r fixed, K(x,y) =xexp(/(r)v/logx + 0(loglog x)2). The proof uses a uniform version of Chernoff s theorem on large deviations from the sample mean of a sum of N independent random variables.

The number of factorizations of numbers less than 𝑥 into factors less than 𝑦