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On the number of positive integers less than ๐‘ฅ and free of prime divisors greater than ๐‘ฅ^{๐‘}

On the number of positive integers less than ๐‘ฅ and free of prime divisors greater than ๐‘ฅ^{๐‘}

recently raised the following question regarding the number of positive integers less than x and free of prime divisors greater than x c t which number is here denoted by f(x, c) : For every fixed positive c, is lim inf x +*>f(xi c)/x>0?This paper, while incidentally answering this question โ€ฆ