Claims

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1982_04_01_ruzsa: Ruzsa determines the logarithmic order of the least number of integers up to x left unsifted by a set of bounded reciprocal sum: yes for C at most 1, no for every C above 1; J. Number Theory (1982), credited by the site.

2023_10_19_weingartner: Weingartner proves that the least unsifted count for reciprocal budget C has exact order x^(e^(1-C)) / log x uniformly for C between 1 and any fixed bound, sharpening Ruzsa; Research in Number Theory (2025), credited by the site.

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