Claims

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2024_03_25_steinerberger: Steinerberger proves that, for all large N, at most 2 to the power 0.93N subsets of one through N have reciprocal sum at most one, so the exact-sum count is not 2 to the power N minus o(N).

2024_04_10_liu_sawhney: Liu and Sawhney prove that the number of subsets of one through N with reciprocal sum one is exp of gamma N plus o(N), with gamma near 0.631573 defined by an integral equation.

2024_04_24_conlon_fox_he_mubayi_pham_suk_verstraete: Conlon, Fox, He, Mubayi, Pham, Suk and Verstraëte prove that the number of subsets of one through N with reciprocal sum one is 2 to the power cN plus o(N), for an explicit constant c near 0.91117.

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