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%I #10 Sep 03 2017 03:26:25
%S 1,3,18,180,12,252,9,324,14580,801900,12150,947700,86240700,821340,
%T 98560800,13404268800,87609600,14981241600,78848640,16558214400,
%U 3824947526400,967711724179200,3506201899200,11687339664,3798385390800
%N a(1) = 1, a(n+1) = a(n)/T(n+1), if T(n+1) divides a(n), else a(n+1) = a(n) *T(n+1), where T(n) = n*(n+1)/2 is a triangular number (A000217).
%H Harvey P. Dale, <a href="/A111465/b111465.txt">Table of n, a(n) for n = 1..1000</a>
%p T:=n->n*(n+1)/2: a[1]:=1: for n from 1 to 28 do if type(a[n]/T(n+1),integer)=true then a[n+1]:=a[n]/T(n+1) else a[n+1]:=a[n]*T(n+1) fi od: seq(a[n],n=1..29); # _Emeric Deutsch_, Aug 11 2005
%t nxt[{n_,a_}]:=Module[{tr=((n+1)(n+2))/2},{n+1,If[Divisible[ a,tr], a/tr,a*tr]}]; Transpose[NestList[nxt,{1,1},30]][[2]] (* _Harvey P. Dale_, Aug 22 2014 *)
%Y Cf. A000217.
%K easy,nonn
%O 1,2
%A _Amarnath Murthy_, Aug 05 2005
%E More terms from _Emeric Deutsch_, Aug 11 2005
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