1,2

It is not possible to have three consecutive refactorable numbers (see the link). The sequence is best viewed in base 12, with X for 10 and E for 11: 1, 8, X68, 25368, 2EX68, 4E768, 97768, X8468, 10EX68, 1X4468, 293768, 34XX68, 3E6768, 504768, 584X68, 887768, X9X468, E27X68, 11X3768, 12E5468, 1397768, 1X49X68, 1XE8468, 2046768, 2383768, 2399X68, 2X12768. After the first two terms all terms are 68, 368, 468, 668, 768, X68 mod 1000 (base 12). - Walter Kehowski (wkehowski(AT)cox.net), Jun 19 2006

No successive refactorables seem to be of the form odd, odd+1. If such a pair exist, they must be very large. The first pair of successive refactorables not divisible by 3 is (5*19)^4-1, (5*19)^4. - Walter Kehowski (wkehowski(AT)cox.net), Jun 25 2006

Eric Weisstein's World of Mathematics, Refactorable Number

a(n) mod tau(a(n)) = 0 and (a(n)+1) mod tau(a(n)+1) = 0 where tau(n) is the number of divisors of n. - Walter Kehowski (wkehowski(AT)cox.net), Jun 19 2006

with(numtheory); RFC:=[]: for w to 1 do for k from 1 to 12^6 do n:=144*k+(6*12+8); if andmap(z-> z mod tau(z) = 0, [n, n+1]) then RFC:=[op(RFC), n]; print(n); fi od od; # it is possible to remove the condition n = (6*12+8) mod 12^2 but you'll get the same sequence. - Walter Kehowski (wkehowski(AT)cox.net), Jun 19 2006

Cf. A033950.

Cf. A033950, A036898, A114617.

Adjacent sequences: A114614 A114615 A114616 this_sequence A114618 A114619 A114620

Sequence in context: A088080 A064073 A096970 this_sequence A017295 A050642 A050648

nonn

Eric Weisstein (eric(AT)weisstein.com), Dec 16, 2005