The number of factorizations of numbers less than x x into divisors greater than y y Academic Article

Let A ( x , y ) A(x,,y) be the number in the title. There is a function h : [ 0 , ) [ 0 , 2 ] h:[0,,infty ) o [0,,2] , decreasing and convex, with h ( 0 ) = 2 h(0) = 2 and lim r h ( r ) = 0 operatorname {lim}_{r o infty }h(r) = 0 , such that if r = log y / log x r = operatorname {log} y/sqrt {operatorname {log} ,x} then as x x o infty with r r fixed, [ A ( x , y ) = C ( r ) x exp ( h ( r ) log