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A287006 a(1) = 1; a(n+1) = Sum_{k=1..n} lcm(a(k),a(n))/a(n).

%I A287006 #18 Jun 21 2018 17:18:23
%S A287006 1,1,2,3,5,8,12,12,13,45,36,32,86,120,75,177,250,315,281,1194,726,925,
%T A287006 2695,2218,5776,6808,6632,8383,28449,34934,53325,69653,153540,107261,
%U A287006 371925,241534,749726,870493,1460599,2623154,3576448,4841995,9911297,15119248,19818816,20257600,7481107,80326829
%N A287006 a(1) = 1; a(n+1) = Sum_{k=1..n} lcm(a(k),a(n))/a(n).
%H A287006 Ivan Neretin, <a href="/A287006/b287006.txt">Table of n, a(n) for n = 1..1000</a>
%H A287006 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%F A287006 a(1) = 1; a(n+1) = Sum_{k=1..n} a(k)/gcd(a(k),a(n)).
%e A287006 a(1) = 1;
%e A287006 a(2) = lcm(a(1),a(1))/a(1) = lcm(1,1)/1 = 1;
%e A287006 a(3) = lcm(a(1),a(2))/a(2) + lcm(a(2),a(2))/a(2) = lcm(1,1)/1 + lcm(1,1)/1 = 2;
%e A287006 a(4) = lcm(a(1),a(3))/a(3) + lcm(a(2),a(3))/a(3) + lcm(a(3),a(3))/a(3) = lcm(1,2)/2 + lcm(1,2)/2 + lcm(2,2)/2 = 3, etc.
%t A287006 a[1] = 1; a[n_] := a[n] = Sum[LCM[a[k - 1], a[n - 1]]/a[n - 1], {k, 2, n}]; Table[a[n], {n, 48}]
%t A287006 a[1] = 1; a[n_] := a[n] = Sum[a[k - 1]/GCD[a[k - 1], a[n - 1]], {k, 2, n}]; Table[a[n], {n, 48}]
%Y A287006 Cf. A056147, A057661, A286946.
%K A287006 nonn
%O A287006 1,3
%A A287006 _Ilya Gutkovskiy_, Aug 31 2017