A287006 - OEIS

%I #18 Jun 21 2018 17:18:23

%S 1,1,2,3,5,8,12,12,13,45,36,32,86,120,75,177,250,315,281,1194,726,925,

%T 2695,2218,5776,6808,6632,8383,28449,34934,53325,69653,153540,107261,

%U 371925,241534,749726,870493,1460599,2623154,3576448,4841995,9911297,15119248,19818816,20257600,7481107,80326829

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

%H Ivan Neretin, <a href="/A287006/b287006.txt">Table of n, a(n) for n = 1..1000</a>

%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),a(n)).

%e a(1) = 1;

%e a(2) = lcm(a(1),a(1))/a(1) = lcm(1,1)/1 = 1;

%e 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 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 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 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 Cf. A056147, A057661, A286946.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Aug 31 2017