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%I #12 Oct 01 2020 12:56:25
%S 1,1,2,6,24,120,840,6720,60480,604800,6652800,86486400,1210809600,
%T 18162144000,308756448000,4940103168000,88921857024000,
%U 1689515283456000,35479820952576000,780556060956672000,17952789402003456000
%N a(1) = 1, a(k) divides a(k+r) for all k and r and the ratios a(k+r)/a(k) are all different.
%e a(7) != 120*1, 120*2, ..., 120*6 as the ratios 1,2,3,...,6 appeared as 1/1, 2/1, 6/2, 24/6, 120/24, 6/1. So a(7) = 7*120 = 840.
%t f[l_List] := Block[{n = Length[l], w, k = 1, r = l[[ -1]]/l},w = Flatten[Table[Take[l, i - n]/l[[i]], {i, n}]];While[Intersection[w, k*r] != {}, k++ ];Append[l, k*l[[ -1]]]];Nest[f, {1}, 21] (* _Ray Chandler_, Feb 08 2007 *)
%Y Cf. A000045, A066720, A079852, A036241.
%K nonn
%O 1,3
%A _Amarnath Murthy_, Feb 19 2003
%E Corrected and extended by Fung Cheok Yin (cheokyin_restart(AT)yahoo.com.hk), Sep 30 2006
%E Edited and further extended by _Ray Chandler_, Feb 08 2007