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A360779
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Refactorable numbers gaps: differences between consecutive refactorable numbers.
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0
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1, 6, 1, 3, 6, 6, 12, 4, 16, 4, 12, 8, 4, 4, 8, 8, 4, 20, 4, 4, 16, 4, 24, 4, 20, 21, 3, 4, 8, 8, 4, 24, 12, 8, 32, 16, 4, 12, 12, 4, 8, 12, 28, 17, 3, 4, 2, 18, 4, 8, 8, 4, 12, 12, 20, 24, 4, 4, 16, 16, 12, 13, 7, 4, 4, 24, 8, 12, 24, 4, 8, 12, 44, 16, 12, 4, 16, 4, 24
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OFFSET
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1,2
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COMMENTS
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Empirically it looks as though the consecutive refactorable numbers >= 8 with odd gaps between them always occur in triples: [8, 9, 12], [204, 225, 228], [424, 441, 444], [612, 625, 632], [1068, 1089, 1096], [1520, 1521, 1524], and so on. The sum of the gaps in the triple is divisible by 4. The middle term of a triple is an odd refactorable number, see A036896.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 2 - 1 = 1;
a(2) = 8 - 2 = 6;
a(3) = 9 - 8 = 1;
and so on.
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MATHEMATICA
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Differences[Select[Range[1000], Divisible[#, DivisorSigma[0, #]] &]] (* Amiram Eldar, Feb 20 2023 *)
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PROG
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(PARI) lista(nn) = my(v=select(x->!(x % numdiv(x)), [1..nn])); vector(#v-1, k, v[k+1]-v[k]); \\ Michel Marcus, Feb 20 2023
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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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