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 A036898 List of pairs of consecutive refactorable numbers. 12
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Donovan Johnson, Table of n, a(n) for n = 1..2000 S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2. S. Colton, HR - Automatic Theory Formation in Pure Mathematics Joshua Zelinsky, Tau Numbers: A Partial Proof of a Conjecture and Other Results, Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.8. EXAMPLE 8 is refactorable because tau(8)=4 and 4 divides 8. 9 is refactorable because tau(9)=3 and 3 divides 9. MATHEMATICA SequencePosition[Table[If[Divisible[n, DivisorSigma[0, n]], 1, 0], {n, 27*10^5}], {1, 1}]//Flatten (* Harvey P. Dale, Dec 07 2021 *) PROG (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 CROSSREFS Cf. A033950, A114617. Sequence in context: A350454 A109351 A111134 * A053372 A088155 A005876 Adjacent sequences: A036895 A036896 A036897 * A036899 A036900 A036901 KEYWORD nonn AUTHOR Simon Colton (simonco(AT)cs.york.ac.uk) STATUS approved

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Last modified August 7 03:39 EDT 2024. Contains 375008 sequences. (Running on oeis4.)