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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
S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.
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
Sequence in context: A350454 A109351 A111134 * A053372 A088155 A005876
KEYWORD
nonn
AUTHOR
Simon Colton (simonco(AT)cs.york.ac.uk)
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)