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.
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
KEYWORD
nonn
AUTHOR
Simon Colton (simonco(AT)cs.york.ac.uk)
STATUS
approved