Claims

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1951_01_01_erdos: Erdős's 1951 paper sketches for alpha = 2, and asserts for alpha below a constant between 2 and 3, that the alpha-th moment of the gaps between consecutive squarefree numbers up to x is asymptotic to a constant times x; Hooley and Chan cite it for every 0 <= alpha <= 2, which answers the problem yes in that range.

1973_12_01_hooley: Hooley's 1973 paper in the Canadian Journal of Mathematics extends Erdős's asymptotic for the alpha-th moment of squarefree gaps from 0 <= alpha <= 2 to 0 <= alpha <= 3, which answers the problem yes in that range.

1997_01_30_huxley: Huxley's chapter in the 1997 Cardiff proceedings proves the asymptotic for the alpha-th moment of squarefree gaps for every 0 <= alpha < 11/3; no refereeing of the volume is on record, so the claim is pending.

1998_01_01_granville: Granville's 1998 paper derives from the abc conjecture the asymptotic, predicted by Erdős, for every moment of the gaps between consecutive squarefree numbers; the hypothesis is unproven, so the page derives nothing.

2023_10_12_chan: Chan's Theorem 1 of 2023 proves the asymptotic for the alpha-th moment of the gaps between consecutive squarefree numbers for every 0 <= alpha < 3.75, the widest unconditional range; refereed in Mosc. J. Comb. Number Theory.

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