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a(n) is found from a(n-1) by dividing by D-1 and multiplying by D, where D is the smallest number that is not a divisor of a(n-1).
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%I #8 Sep 13 2015 21:08:33

%S 1,2,3,6,8,12,15,30,40,60,70,105,210,280,420,480,560,840,945,1890,

%T 2520,2772,3465,6930,9240,10395,20790,27720,30030,40040,60060,68640,

%U 80080,120120,135135,270270,360360,384384,480480,540540,617760,720720,765765

%N a(n) is found from a(n-1) by dividing by D-1 and multiplying by D, where D is the smallest number that is not a divisor of a(n-1).

%e Smallest number not a factor of 30 is 4, so next term after 30 is (30/3)*4 = 40.

%p A133582 := proc(n) option remember ; local d ; if n = 1 then 1; else for d from 2 do if A133582(n-1) mod d <> 0 then RETURN( A133582(n-1)*d/(d-1) ) ; fi ; od; fi ; end: seq(A133582(n),n=1..40) ; # _R. J. Mathar_, Jan 07 2008

%t a = {1, 2}; Do[i = 1; While[IntegerQ[a[[ -1]]/i], i++ ]; AppendTo[a, (i/(i - 1))*a[[ -1]]], {50}]; a (* _Stefan Steinerberger_, Dec 29 2007 *)

%t nxt[n_]:=Module[{d=First[Complement[Range[n],Divisors[n]]]},d/(d-1)*n]; Join[{1,2},NestList[nxt,3,50]] (* _Harvey P. Dale_, Jul 10 2012 *)

%K nonn

%O 1,2

%A _J. Lowell_, Dec 26 2007

%E More terms from _Stefan Steinerberger_, Dec 29 2007