A079854 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.
1, 1, 2, 6, 24, 120, 840, 6720, 60480, 604800, 6652800, 86486400, 1210809600, 18162144000, 308756448000, 4940103168000, 88921857024000, 1689515283456000, 35479820952576000, 780556060956672000, 17952789402003456000
Offset: 1
Keywords
Examples
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.
Programs
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Mathematica
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 *)
Extensions
Corrected and extended by Fung Cheok Yin (cheokyin_restart(AT)yahoo.com.hk), Sep 30 2006
Edited and further extended by Ray Chandler, Feb 08 2007