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A036898
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List of pairs of consecutive refactorable numbers.
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12
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1, 2, 8, 9, 1520, 1521, 50624, 50625, 62000, 62001, 103040, 103041, 199808, 199809, 221840, 221841, 269360, 269361, 463760, 463761, 690560, 690561, 848240, 848241, 986048, 986049, 1252160, 1252161, 1418480, 1418481, 2169728, 2169729, 2692880
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OFFSET
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1,2
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COMMENTS
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Zelinsky (2002, Theorem 59, p. 15) proved that if k > 1, k and k+1 are both refactorable numbers, then k is even. As a result, a(n) == n-1 (mod 2) for n >= 3. See also A114617. - Jianing Song, Apr 01 2021
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LINKS
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EXAMPLE
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8 is refactorable because tau(8)=4 and 4 divides 8.
9 is refactorable because tau(9)=3 and 3 divides 9.
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MATHEMATICA
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SequencePosition[Table[If[Divisible[n, DivisorSigma[0, n]], 1, 0], {n, 27*10^5}], {1, 1}]//Flatten (* Harvey P. Dale, Dec 07 2021 *)
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PROG
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(PARI) isrefac(n) = ! (n % numdiv(n));
lista(nn) = {for (n = 1, nn, if (isrefac(n) && isrefac(n+1), print1(n, ", ", n+1, ", ")); ); } \\ Michel Marcus, Aug 31 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Simon Colton (simonco(AT)cs.york.ac.uk)
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STATUS
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approved
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