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%I #8 Sep 15 2017 11:43:26
%S 1,1,2,4,4,12,9,33,50,78,99,173,264,658,570,1056,1099,4113,2443,10129,
%T 18866,23226,39775,102665,171529,256039,610467,815809,1795028,3854202,
%U 3044396,10752800,5509162,22665306,25847226,66558954,25219183,167266731,264535960,163511658,346473322,1109093102
%N a(1) = 1; a(n+1) = Sum_{k=1..n} lcm(a(k),n)/n.
%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%F a(1) = 1; a(n+1) = Sum_{k=1..n} a(k)/gcd(a(k),n).
%e a(1) = 1;
%e a(2) = lcm(a(1),1)/1 = lcm(1,1)/1 = 1;
%e a(3) = lcm(a(1),2)/2 + lcm(a(2),2)/2 = lcm(1,2)/2 + lcm(1,2)/2 = 2;
%e a(4) = lcm(a(1),3)/3 + lcm(a(2),3)/3 + lcm(a(3),3)/3 = lcm(1,3)/3 + lcm(1,3)/3 + lcm(2,3)/3 = 4, etc.
%t a[1] = 1; a[n_] := a[n] = Sum[LCM[a[k - 1], n - 1]/(n - 1), {k, 2, n}]; Table[a[n], {n, 42}]
%t a[1] = 1; a[n_] := a[n] = Sum[a[k - 1]/GCD[a[k - 1], n - 1], {k, 2, n}]; Table[a[n], {n, 42}]
%Y Cf. A056147, A057661, A286946, A287006.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Sep 14 2017