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a(1) = 1, a(n) = lcm(n, a(n-1)) / gcd(n, a(n-1)).
1

%I #9 Nov 17 2018 21:54:21

%S 1,2,6,6,30,5,35,280,2520,252,2772,231,3003,858,1430,5720,97240,

%T 437580,8314020,415701,969969,176358,4056234,2704156,67603900,2600150,

%U 70204050,10029150,290845350,9694845,300540195,9617286240,35263382880,1037158320

%N a(1) = 1, a(n) = lcm(n, a(n-1)) / gcd(n, a(n-1)).

%e a(5) = 30 because given a(4) = 6: lcm(5, 6) / gcd(5, 6) = 30 / 1 = 30.

%t k = 1; Print[k]; Do[k = LCM[n, k] / GCD[n, k]; Print[k], {n, 2, 30}] (* _Ryan Propper_, Jun 19 2005 *)

%t nxt[{n_,a_}]:={n+1,LCM[n+1,a]/GCD[n+1,a]}; Transpose[NestList[nxt,{1,1},40]] [[2]] (* _Harvey P. Dale_, Mar 07 2013 *)

%Y Essentially a duplicate of A008339, which is the main entry for this sequence.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Oct 30 2002

%E Corrected and extended by _Ryan Propper_, Jun 19 2005