A292303 a(1) = 1; a(n+1) = Sum_{k=1..n} lcm(a(k),n)/n.

1, 1, 2, 4, 4, 12, 9, 33, 50, 78, 99, 173, 264, 658, 570, 1056, 1099, 4113, 2443, 10129, 18866, 23226, 39775, 102665, 171529, 256039, 610467, 815809, 1795028, 3854202, 3044396, 10752800, 5509162, 22665306, 25847226, 66558954, 25219183, 167266731, 264535960, 163511658, 346473322, 1109093102

Offset

1,3

Links

Table of n, a(n) for n=1..42.

Index entries for sequences related to lcm's

Formula

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

Example

a(1) = 1;
a(2) = lcm(a(1),1)/1 = lcm(1,1)/1 = 1;
a(3) = lcm(a(1),2)/2 + lcm(a(2),2)/2 = lcm(1,2)/2 + lcm(1,2)/2 = 2;
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.

Mathematica

a[1] = 1; a[n_] := a[n] = Sum[LCM[a[k - 1], n - 1]/(n - 1), {k, 2, n}]; Table[a[n], {n, 42}]
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}]

Crossrefs

Cf. A056147, A057661, A286946, A287006.

Sequence in context: A225232 A326824 A319210 * A000936 A376091 A319594

Adjacent sequences: A292300 A292301 A292302 * A292304 A292305 A292306

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 14 2017

Status

approved