Asymptotics are derived for the number of integers in bad or very bad consecutive intervals, with near-asymptotics for type F3 interval endpoints and solutions to a1! a2! a3! = m².
Ramachandra,A Note on Numbers with a Large Prime Factor, Journal of the London Mathematical Society, s2-1 (1969), 303–306
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Products of consecutive integers with unusual anatomy
Asymptotics are derived for the number of integers in bad or very bad consecutive intervals, with near-asymptotics for type F3 interval endpoints and solutions to a1! a2! a3! = m².