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A343817
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Refactorable numbers (A033950) which set a record for the gap to the next refactorable number.
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0
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1, 2, 24, 40, 108, 156, 296, 732, 1692, 31616, 51608, 568720, 766620, 6195132, 6938752, 17879440, 18578320, 35196584, 228694176, 475292728, 589169184, 1451254356, 3252050592, 4865544096, 6328305120, 8082626976, 8694028264, 9112984448, 30328732568, 46093418640
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OFFSET
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1,2
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COMMENTS
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Since the asymptotic density of the refactorable numbers is 0 (Kennedy and Cooper, 1990), this sequence is infinite.
The corresponding record values are 1, 6, 12, 16, 20, 24, 32, 44, 92, 100, 144, 152, 180, 192, 208, 212, 236, 268, 280, 296, 336, 360, 368, 372, 384, 396, 408, 432, 488, 496, ...
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LINKS
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EXAMPLE
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The first 8 refactorable numbers are 1, 2, 8, 9, 12, 18, 24 and 36. The gaps between them are 1, 6, 1, 3, 6, 6 and 12. The record gaps, 1, 6 and 12, occur after the refactorable numbers 1, 2 and 24, which are the first 3 terms of this sequence.
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MATHEMATICA
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refQ[n_] := Divisible[n, DivisorSigma[0, n]]; seq = {}; m = 1; dm = 0; Do[If[refQ[n], d = n - m; If[d > dm, dm = d; AppendTo[seq, m]]; m = n], {n, 2, 10^6}]; seq
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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