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

1, 1, 2, 3, 5, 8, 12, 12, 13, 45, 36, 32, 86, 120, 75, 177, 250, 315, 281, 1194, 726, 925, 2695, 2218, 5776, 6808, 6632, 8383, 28449, 34934, 53325, 69653, 153540, 107261, 371925, 241534, 749726, 870493, 1460599, 2623154, 3576448, 4841995, 9911297, 15119248, 19818816, 20257600, 7481107, 80326829

Offset

1,3

Links

Ivan Neretin, Table of n, a(n) for n = 1..1000

Index entries for sequences related to lcm's

Formula

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

Example

a(1) = 1;
a(2) = lcm(a(1),a(1))/a(1) = lcm(1,1)/1 = 1;
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;
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.

Mathematica

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}]
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}]

Crossrefs

Cf. A056147, A057661, A286946.

Sequence in context: A105766 A056695 A342746 * A020899 A057987 A243165

Adjacent sequences: A287003 A287004 A287005 * A287007 A287008 A287009

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 31 2017

Status

approved