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A265574 LCM-transform of triangular numbers.

%I A265574 #22 Apr 11 2020 14:58:01
%S A265574 1,3,2,5,1,7,2,3,1,11,1,13,1,1,2,17,1,19,1,1,1,23,1,5,1,3,1,29,1,31,2,
%T A265574 1,1,1,1,37,1,1,1,41,1,43,1,1,1,47,1,7,1,1,1,53,1,1,1,1,1,59,1,61,1,1,
%U A265574 2,1,1,67,1,1,1,71,1,73,1,1,1,1,1,79,1,3,1,83,1,1,1,1,1,89,1,1,1,1,1,1,1,97,1
%N A265574 LCM-transform of triangular numbers.
%H A265574 A. Nowicki, <a href="http://arxiv.org/abs/1310.2416">Strong divisibility and LCM-sequences</a>, arXiv:1310.2416 [math.NT], 2013.
%H A265574 A. Nowicki, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.122.10.958">Strong divisibility and LCM-sequences</a>, Am. Math. Mnthly 122 (2015), 958-966.
%F A265574 From _Andrey Zabolotskiy_, Apr 11 2020: (Start)
%F A265574 a(n) = A051543(n-1) for n>1.
%F A265574 a(n) = A014963(n+1) for n>1. (End)
%p A265574 LCMXfm:=proc(a) local L,i,n,g,b;
%p A265574 L:=nops(a);
%p A265574 g:=Array(1..L,0); b:=Array(1..L,0);
%p A265574 b[1]:=a[1]; g[1]:=a[1];
%p A265574 for n from 2 to L do g[n]:=ilcm(g[n-1],a[n]); b[n]:=g[n]/g[n-1]; od;
%p A265574 lprint([seq(b[i],i=1..L)]);
%p A265574 end;
%p A265574 t1:=[seq(n*(n+1)/2,n=1..100)];
%p A265574 LCMXfm(t1);
%t A265574 LCMXfm[a_List] := Module[{L = Length[a], b, g}, b[1] = g[1] = a[[1]]; b[_] = 0; g[_] = 0; Do[g[n] = LCM[g[n - 1], a[[n]]]; b[n] = g[n]/g[n - 1], {n, 2, L}]; Array[b, L]];
%t A265574 LCMXfm[Table[n*(n + 1)/2, {n, 1, 100}]] (* _Jean-François Alcover_, Dec 05 2017, from Maple *)
%Y A265574 Cf. A051543, A020500, A014963.
%K A265574 nonn
%O A265574 1,2
%A A265574 _N. J. A. Sloane_, Jan 02 2016