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Published online by Cambridge University Press: 20 June 2023
We use bounds of character sums and some combinatorial arguments to show the abundance of very smooth numbers which also have very few nonzero binary digits.
This work started during a very enjoyable visit by the authors to the Max Planck Institute for Mathematics, Bonn, whose hospitality and support is very much appreciated. During the preparation of this work, I.S. was also supported in part by the Australian Research Council Grant DP200100355.