Abstract
For integer n and real u, define Δ(n,u)≔|{d:d∣n,eu<d⩽eu+1}|. Then, the Erdős–Hooley Delta function is defined as Δ(n)≔maxu∈RΔ(n,u). We provide uniform upper and lower bounds for the mean-value of Δ(n) over friable integers, i.e. integers free of large prime factors.
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